Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young
2017-03-14
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems
Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim
2012-01-01
Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.
Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems
Woolley, Thomas E.
2012-05-22
Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.
Stochastic reaction-diffusion algorithms for macromolecular crowding
Sturrock, Marc
2016-06-01
Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.
Lecca, Paola; Morpurgo, Daniele
2012-01-01
Reaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel. We present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non
Wang, Xiaohu; Lu, Kening; Wang, Bixiang
2018-01-01
In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction-diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction-diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction-diffusion equation for both additive and multiplicative noise.
Stochastic flows, reaction-diffusion processes, and morphogenesis
International Nuclear Information System (INIS)
Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.
1983-01-01
Recently, an exact procedure has been introduced [C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)] for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processs in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d = 2,3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of ''mixing'' by showing that the degree of chaos associated with flows in certain lattice-systems can be calibrated by monitoring the lattice walks induced by the Poincare map of a certain parabolic function
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen
2015-01-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Nonlinear analysis of a reaction-diffusion system: Amplitude equations
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2012-10-15
A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.
An adaptive algorithm for simulation of stochastic reaction-diffusion processes
International Nuclear Information System (INIS)
Ferm, Lars; Hellander, Andreas; Loetstedt, Per
2010-01-01
We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
Multi-scale simulation of reaction-diffusion systems
Vijaykumar, A.
2017-01-01
In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function
Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Li Wan
2012-01-01
Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.
2011-10-19
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
International Nuclear Information System (INIS)
Wang Linshan; Zhang Zhe; Wang Yangfan
2008-01-01
Some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks. The criteria are computationally efficient, since they are in the forms of some linear matrix inequalities
Distribution in flowing reaction-diffusion systems
Kamimura, Atsushi; Herrmann, Hans J.; Ito, Nobuyasu
2009-01-01
A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.
Distribution in flowing reaction-diffusion systems
Kamimura, Atsushi
2009-12-28
A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.
Pattern formation in reaction diffusion systems with finite geometry
International Nuclear Information System (INIS)
Borzi, C.; Wio, H.
1990-04-01
We analyze the one-component, one-dimensional, reaction-diffusion equation through a simple inverse method. We confine the system and fix the boundary conditions as to induce pattern formation. We analyze the stability of those patterns. Our goal is to get information about the reaction term out of the preknowledgment of the pattern. (author). 5 refs
Analytically solvable models of reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Reaction-diffusion systems in intracellular molecular transport and control.
Soh, Siowling; Byrska, Marta; Kandere-Grzybowska, Kristiana; Grzybowski, Bartosz A
2010-06-07
Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.
Parametric spatiotemporal oscillation in reaction-diffusion systems.
Ghosh, Shyamolina; Ray, Deb Shankar
2016-03-01
We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.
Turing Patterns in a Reaction-Diffusion System
International Nuclear Information System (INIS)
Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang
2006-01-01
We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.
Energy Technology Data Exchange (ETDEWEB)
Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan); Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610 (Belgium); Chen, W. [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan)
2016-08-07
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.
A Weak Comparison Principle for Reaction-Diffusion Systems
Directory of Open Access Journals (Sweden)
José Valero
2012-01-01
Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.
Global dynamics of a reaction-diffusion system
Directory of Open Access Journals (Sweden)
Yuncheng You
2011-02-01
Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.
Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn
Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han
2018-06-01
We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Pattern dynamics of the reaction-diffusion immune system.
Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie
2018-01-01
In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.
Control of transversal instabilities in reaction-diffusion systems
Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald
2018-05-01
In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.
Decay to Equilibrium for Energy-Reaction-Diffusion Systems
Haskovec, Jan
2018-02-06
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.
Decay to Equilibrium for Energy-Reaction-Diffusion Systems
Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter A.; Mielke, Alexander
2018-01-01
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.
Rethinking pattern formation in reaction-diffusion systems
Halatek, J.; Frey, E.
2018-05-01
The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.; Chapman, S. J.; Erban, R.
2011-01-01
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches
Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
Krause, Andrew L.; Klika, Václav; Woolley, Thomas E.; Gaffney, Eamonn A.
2018-05-01
We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well-known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity.
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2014-08-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables
Pattern formation in three-dimensional reaction-diffusion systems
Callahan, T. K.; Knobloch, E.
1999-08-01
Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.
Reaction diffusion in chromium-zircaloy-2 system
International Nuclear Information System (INIS)
Xiang Wenxin; Ying Shihao
2001-01-01
Reaction diffusion in the chromium-zircaloy-2 diffusion couples is investigated in the temperature range of 1023 - 1123 K. Scanning electron microscope (SEM) and energy dispersive spectrum (EDS) were used to measure the thickness of the reaction layer and to determine the Zr, Fe and Cr concentration penetrate profile in reaction layer, respectively. The growth kinetics of reaction layer has been studied and the results show that the growth of intermetallic compound is controlled by the process of volume diffusion as the layer growth approximately obeys the parabolic law. Interdiffusion coefficients were calculated using Boltzmann-Matano-Heumann model. Calculated interdiffusion coefficients were compared with those obtained on the condition that Cr dissolves in Zr and merely forms dilute solid solution. The comparison indicates that Cr diffuses in dilute solid solution is five orders of magnitude faster than in Zr(Fe, Cr) 2 intermetallic compound
Amplitude equations for a sub-diffusive reaction-diffusion system
International Nuclear Information System (INIS)
Nec, Y; Nepomnyashchy, A A
2008-01-01
A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points
Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system
International Nuclear Information System (INIS)
Abdusalam, H.A; Fahmy, E.S.
2003-01-01
It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar
2018-02-01
We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.
International Nuclear Information System (INIS)
Moore, Peter K.
2003-01-01
Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied
International Nuclear Information System (INIS)
Cherniha, Roman
2010-01-01
New definitions of Q-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of Q-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. A class of two-component nonlinear reaction-diffusion systems is examined to demonstrate the applicability of the definitions proposed and it is shown when different definitions of Q-conditional symmetry lead to the same operators.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.; Fellner, K.; Markowich, P. A
2008-01-01
and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid
Traveling wave solutions for reaction-diffusion systems
DEFF Research Database (Denmark)
Lin, Zhigui; Pedersen, Michael; Tian, Canrong
2010-01-01
This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems...... with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions...
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif; Ritter, Laura; Walton, Jay R.
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure
Muntean, A.
2009-01-01
Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved, giving conditions on system parameters guaranteeing stability of the health state, and a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation. © 2010 Society for Industrial and Applied Mathematics.
International Nuclear Information System (INIS)
Mittal, R.C.; Rohila, Rajni
2016-01-01
In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.
Delay-induced wave instabilities in single-species reaction-diffusion systems
Otto, Andereas; Wang, Jian; Radons, Günter
2017-11-01
The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida; Gaffney, Eamonn A.; Maini, Philip K.
2009-01-01
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida
2009-08-29
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.
Dichotomous-noise-induced pattern formation in a reaction-diffusion system
Das, Debojyoti; Ray, Deb Shankar
2013-06-01
We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.
Externally controlled anisotropy in pattern-forming reaction-diffusion systems.
Escala, Dario M; Guiu-Souto, Jacobo; Muñuzuri, Alberto P
2015-06-01
The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
International Nuclear Information System (INIS)
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-01-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society
Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.
Wang, Hongli; Ouyang, Qi
2007-11-23
The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.
Existence and exponential stability of traveling waves for delayed reaction-diffusion systems
Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian
2018-03-01
The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-04-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi
2014-04-11
Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming
Mielke, Alexander; Mittnenzweig, Markus
2018-04-01
We discuss how the recently developed energy dissipation methods for reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions, we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method.
Square Turing patterns in reaction-diffusion systems with coupled layers
Energy Technology Data Exchange (ETDEWEB)
Li, Jing [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); Ouyang, Qi, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); The Peking-Tsinghua Center for Life Sciences, Beijing 100871 (China)
2014-06-15
Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
International Nuclear Information System (INIS)
Owolabi, Kolade M.
2016-01-01
The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.
Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner
2017-01-01
We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.
Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems
International Nuclear Information System (INIS)
Trueba, J L; Arrayas, M
2009-01-01
We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumo model. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement. (fast track communication)
Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Trueba, J L; Arrayas, M [Area de Electromagnetismo, Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid (Spain)
2009-07-17
We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumo model. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement. (fast track communication)
Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay
Dong, Tao; Xia, Linmao
2017-12-01
In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.
Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation
Chern, Jann-Long; Morita, Yoshihisa; Shieh, Tien-Tsan
2018-01-01
We deal with a stationary problem of a reaction-diffusion system with a conservation law under the Neumann boundary condition. It is shown that the stationary problem turns to be the Euler-Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0 , 1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coefficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κ satisfying the relation ε : =√{ d } =√{ log κ } /κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κ the asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.
Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system
International Nuclear Information System (INIS)
He Zhizhu; Liu, Jing
2010-01-01
This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.
Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.
Maybank, Philip J; Whiteley, Jonathan P
2014-02-01
Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.
Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition
Ódor, G
2003-01-01
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
Anomalous dimension in a two-species reaction-diffusion system
Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.
2018-01-01
We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \
Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective
Locke, Rory A.; Mahoney, John R.; Mitchell, Kevin A.
2018-01-01
Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.
Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks
Kouvaris, Nikos E.; Kori, Hiroshi; Mikhailov, Alexander S.
2012-01-01
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed. PMID:23028746
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Väth, Martin
2016-01-01
Roč. 61, č. 1 (2016), s. 1-25 ISSN 0862-7940 R&D Projects: GA ČR GA13-12580S Institutional support: RVO:67985904 ; RVO:67985840 Keywords : reaction-diffusion system * unlateral condition * variational inequality Subject RIV: EG - Zoology; BA - General Mathematics (MU-W) Impact factor: 0.618, year: 2016
Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems
International Nuclear Information System (INIS)
Bernoff, A.J.; Kuske, R.; Matkowsky, B.J.; Volpert, V.
1995-01-01
In many problems, one observes traveling waves that propagate with constant velocity and shape in the χ direction, say, are independent of y, and z and describe transitions between two equilibrium states. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario the authors consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. They determine solutions bifurcating from the basic state that describe counterpropagating traveling wave in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, they derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave they demonstrate that it is sufficient to consider the cases of (1) purely transverse perturbations, (2) purely longitudinal perturbations, and (3) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
Directory of Open Access Journals (Sweden)
Said Kouachi
2001-10-01
Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].
Boundedness for a system of reaction-diffusion equations with more general Arrhenius term. Pt. 1
International Nuclear Information System (INIS)
Okoya, S.S.
1992-11-01
In this paper, we consider an extended model of a coupled nonlinear reaction-diffusion equation with Neumann-Neumann boundary conditions. We obtain upper linear growth bound for one of the components. We also find the corresponding bound for the case of Dirichlet-Dirichlet boundary conditions. (author). 12 refs
International Nuclear Information System (INIS)
Wu Shiliang; Li Wantong
2009-01-01
This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.
International Nuclear Information System (INIS)
Ferreri, J. C.; Carmen, A. del
1998-01-01
A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs
Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics
International Nuclear Information System (INIS)
Windus, Alastair; Jensen, Henrik J
2008-01-01
We consider a reaction-diffusion model incorporating the reactions A→φ, A→2A and 2A→3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.
Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics
Energy Technology Data Exchange (ETDEWEB)
Windus, Alastair; Jensen, Henrik J [The Institute for Mathematical Sciences, 53 Prince' s Gate, South Kensington, London SW7 2PG (United Kingdom)], E-mail: h.jensen@imperial.ac.uk
2008-11-15
We consider a reaction-diffusion model incorporating the reactions A{yields}{phi}, A{yields}2A and 2A{yields}3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
Weise, Louis D; Panfilov, Alexander V
2011-01-01
Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM) model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material) to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
Spiral patterns near Turing instability in a discrete reaction diffusion system
International Nuclear Information System (INIS)
Li, Meifeng; Han, Bo; Xu, Li; Zhang, Guang
2013-01-01
In this paper, linear stability analysis is applied to an exponential discrete Lotka–Volterra system, which describes the competition between two identical species. Conditions for the Turing instability are obtained and the emergence of spiral patterns is demonstrated by means of numerical simulations in the vicinity of the bifurcation point. Moreover, the impact of crucial system parameters on the stability and coherence of spiral patterns is illustrated on several examples
Instability induced by cross-diffusion in reaction-diffusion systems
DEFF Research Database (Denmark)
Tian, Canrong; Lin, Zhigui; Pedersen, Michael
2010-01-01
In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cros...... can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.......In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion...
Lagzi, István; Ueyama, Daishin
2009-01-01
The pattern transition between periodic precipitation pattern formation (Liesegang phenomenon) and pure crystal growth regimes is investigated in silver nitrate and potassium dichromate system in mixed agarose-gelatin gel. Morphologically different patterns were found depending on the quality of the gel, and transition between these typical patterns can be controlled by the concentration of gelatin in mixed gel. Effect of temperature and hydrodynamic force on precipitation pattern structure was also investigated.
Ducrot, Arnaud; Giletti, Thomas
2014-09-01
In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.
Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R2
Niu, Hong-Tao; Wang, Zhi-Cheng; Bu, Zhen-Hui
2018-05-01
In this paper we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in R2 by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in R2.
Spirals in a reaction-diffusion system: Dependence of wave dynamics on excitability
Mahanta, Dhriti; Das, Nirmali Prabha; Dutta, Sumana
2018-02-01
A detailed study of the effects of excitability of the Belousov-Zhabotinsky (BZ) reaction on spiral wave properties has been carried out. Using the Oregonator model, we explore the various regimes of wave activity, from sustained oscillations to wave damping, as the system undergoes a Hopf bifurcation, that is achieved by varying the excitability parameter, ɛ . We also discover a short range of parameter values where random oscillations are observed. With an increase in the value of ɛ , the frequency of the wave decreases exponentially, as the dimension of the spiral core expands. These numerical results are confirmed by carrying out experiments in thin layers of the BZ system, where the excitability is changed by varying the concentrations of the reactant species. Effect of reactant concentrations on wave properties like time period and wavelength are also explored in detail. Drifting and meandering spirals are found in the parameter space under investigation, with the excitability affecting the tip trajectory in a way predicted by the numerical studies. This study acts as a quantitative evidence of the relationship between the excitability parameter, ɛ , and the substrate concentrations.
Spirals in a reaction-diffusion system: Dependence of wave dynamics on excitability.
Mahanta, Dhriti; Das, Nirmali Prabha; Dutta, Sumana
2018-02-01
A detailed study of the effects of excitability of the Belousov-Zhabotinsky (BZ) reaction on spiral wave properties has been carried out. Using the Oregonator model, we explore the various regimes of wave activity, from sustained oscillations to wave damping, as the system undergoes a Hopf bifurcation, that is achieved by varying the excitability parameter, ε. We also discover a short range of parameter values where random oscillations are observed. With an increase in the value of ε, the frequency of the wave decreases exponentially, as the dimension of the spiral core expands. These numerical results are confirmed by carrying out experiments in thin layers of the BZ system, where the excitability is changed by varying the concentrations of the reactant species. Effect of reactant concentrations on wave properties like time period and wavelength are also explored in detail. Drifting and meandering spirals are found in the parameter space under investigation, with the excitability affecting the tip trajectory in a way predicted by the numerical studies. This study acts as a quantitative evidence of the relationship between the excitability parameter, ε, and the substrate concentrations.
Random attractors for stochastic lattice reversible Gray-Scott systems with additive noise
Directory of Open Access Journals (Sweden)
Hongyan Li
2015-10-01
Full Text Available In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.
Reaction-Diffusion Automata Phenomenology, Localisations, Computation
Adamatzky, Andrew
2013-01-01
Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments. This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
Speed ot travelling waves in reaction-diffusion equations
International Nuclear Information System (INIS)
Benguria, R.D.; Depassier, M.C.; Mendez, V.
2002-01-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
International Nuclear Information System (INIS)
Abdelmalek, Salem; Kouachi, Said
2007-01-01
To prove global existence for solutions of m-component reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions and nonhomogeneous Robin boundary conditions. The purpose of this paper is to prove the existence of a global solution using a single inequality for the polynomial growth condition of the reaction terms. Our technique is based on the construction of polynomial functionals. This result generalizes those obtained recently by Kouachi et al (at press), Kouachi (2002 Electron. J. Diff. Eqns 2002 1), Kouachi (2001 Electron. J. Diff. Eqns 2001 1) and independently by Malham and Xin (1998 Commun. Math. Phys. 193 287)
Laser Spot Detection Based on Reaction Diffusion
Alejandro Vázquez-Otero; Danila Khikhlukha; J. M. Solano-Altamirano; Raquel Dormido; Natividad Duro
2016-01-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presente...
Directory of Open Access Journals (Sweden)
Marco A. Velasco
2016-10-01
Full Text Available Scaffolds are essential in bone tissue engineering, as they provide support to cells and growth factors necessary to regenerate tissue. In addition, they meet the mechanical function of the bone while it regenerates. Currently, the multiple methods for designing and manufacturing scaffolds are based on regular structures from a unit cell that repeats in a given domain. However, these methods do not resemble the actual structure of the trabecular bone which may work against osseous tissue regeneration. To explore the design of porous structures with similar mechanical properties to native bone, a geometric generation scheme from a reaction-diffusion model and its manufacturing via a material jetting system is proposed. This article presents the methodology used, the geometric characteristics and the modulus of elasticity of the scaffolds designed and manufactured. The method proposed shows its potential to generate structures that allow to control the basic scaffold properties for bone tissue engineering such as the width of the channels and porosity. The mechanical properties of our scaffolds are similar to trabecular tissue present in vertebrae and tibia bones. Tests on the manufactured scaffolds show that it is necessary to consider the orientation of the object relative to the printing system because the channel geometry, mechanical properties and roughness are heavily influenced by the position of the surface analyzed with respect to the printing axis. A possible line for future work may be the establishment of a set of guidelines to consider the effects of manufacturing processes in designing stages.
Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.
2009-06-01
Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.
International Nuclear Information System (INIS)
Ghorai, Santu; Poria, Swarup
2016-01-01
Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food.
Stochastic runaway of dynamical systems
International Nuclear Information System (INIS)
Pfirsch, D.; Graeff, P.
1984-10-01
One-dimensional, stochastic, dynamical systems are well studied with respect to their stability properties. Less is known for the higher dimensional case. This paper derives sufficient and necessary criteria for the asymptotic divergence of the entropy (runaway) and sufficient ones for the moments of n-dimensional, stochastic, dynamical systems. The crucial implication is the incompressibility of their flow defined by the equations of motion in configuration space. Two possible extensions to compressible flow systems are outlined. (orig.)
Stochastic Models of Polymer Systems
2016-01-01
Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...ADDRESS. Princeton University PO Box 0036 87 Prospect Avenue - 2nd floor Princeton, NJ 08544 -2020 14-Mar-2014 ABSTRACT Number of Papers published in...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title
Functional Abstraction of Stochastic Hybrid Systems
Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.
2006-01-01
The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways
Stochastic cooling system in COSY
International Nuclear Information System (INIS)
Brittner, P.; Hacker, H.U.; Prasuhn, D.; Schug, G.; Singer, H.; Spiess, W.; Stassen, R.
1994-01-01
The stochastic cooler system in COSY is designed for proton kinetic energies between 0.8 and 2.5 GeV. Fabrication of the mechanical parts of the system is going on. Test results of the prototype measurements as well as data of the active RF-compontens are presented. (orig.)
Stochastic cooling system in COSY
Energy Technology Data Exchange (ETDEWEB)
Brittner, P [Forschungszentrum Juelich GmbH (Germany); Hacker, H U [Forschungszentrum Juelich GmbH (Germany); Prasuhn, D [Forschungszentrum Juelich GmbH (Germany); Schug, G [Forschungszentrum Juelich GmbH (Germany); Singer, H [Forschungszentrum Juelich GmbH (Germany); Spiess, W [Forschungszentrum Juelich GmbH (Germany); Stassen, R [Forschungszentrum Juelich GmbH (Germany)
1994-09-01
The stochastic cooler system in COSY is designed for proton kinetic energies between 0.8 and 2.5 GeV. Fabrication of the mechanical parts of the system is going on. Test results of the prototype measurements as well as data of the active RF-compontens are presented. (orig.)
Stochastic Modelling of Hydrologic Systems
DEFF Research Database (Denmark)
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....
Laser Spot Detection Based on Reaction Diffusion.
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad
2016-03-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
Laser Spot Detection Based on Reaction Diffusion
Directory of Open Access Journals (Sweden)
Alejandro Vázquez-Otero
2016-03-01
Full Text Available Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
Diffusive instabilities in hyperbolic reaction-diffusion equations
Zemskov, Evgeny P.; Horsthemke, Werner
2016-03-01
We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu, Luminita Manuela
2012-01-01
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
International Nuclear Information System (INIS)
Garcia Velarde, M.
1977-01-01
Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es
International Nuclear Information System (INIS)
Garcia Velarde, M.
1977-01-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs
Stochastic analysis of biochemical systems
Anderson, David F
2015-01-01
This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...
Laser spot detection based on reaction diffusion
Czech Academy of Sciences Publication Activity Database
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, R.; Duro, N.
2016-01-01
Roč. 16, č. 3 (2016), s. 1-11, č. článku 315. ISSN 1424-8220 R&D Projects: GA MŠk EF15_008/0000162 Grant - others:ELI Beamlines(XE) CZ.02.1.01/0.0/0.0/15_008/0000162 Institutional support: RVO:68378271 Keywords : laser spot detection * laser beam detection * reaction diffusion models * Fitzhugh-Nagumo model * reaction diffusion computation * Turing patterns Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.677, year: 2016
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Safety Analysis of Stochastic Dynamical Systems
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...... that shows how the p-safe initial set is computed numerically....
An Application of Equivalence Transformations to Reaction Diffusion Equations
Directory of Open Access Journals (Sweden)
Mariano Torrisi
2015-10-01
Full Text Available In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.
Molecular finite-size effects in stochastic models of equilibrium chemical systems.
Cianci, Claudia; Smith, Stephen; Grima, Ramon
2016-02-28
The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.
Stochastic properties of the Friedman dynamical system
International Nuclear Information System (INIS)
Szydlowski, M.; Heller, M.; Golda, Z.
1985-01-01
Some mathematical aspects of the stochastic cosmology are discussed in the corresponding ordinary Friedman world models. In particulare, it is shown that if the strong and Lorentz energy conditions are known, or the potential function is given, or a stochastic measure is suitably defined then the structure of the phase plane of the Friedman dynamical system is determined. 11 refs., 2 figs. (author)
Reaction diffusion equations with boundary degeneracy
Directory of Open Access Journals (Sweden)
Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Stochastic Thermodynamics: A Dynamical Systems Approach
Directory of Open Access Journals (Sweden)
Tanmay Rajpurohit
2017-12-01
Full Text Available In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.
Modeling and analysis of stochastic systems
Kulkarni, Vidyadhar G
2011-01-01
Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi
Glider-based computing in reaction-diffusion hexagonal cellular automata
International Nuclear Information System (INIS)
Adamatzky, Andrew; Wuensche, Andrew; De Lacy Costello, Benjamin
2006-01-01
A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space-time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton
Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas
2016-01-01
Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Reaction diffusion and solid state chemical kinetics handbook
Dybkov, V I
2010-01-01
This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate
Reaction-diffusion pulses: a combustion model
International Nuclear Information System (INIS)
Campos, Daniel; Llebot, Josep Enric; Fort, Joaquim
2004-01-01
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations
Reaction-diffusion pulses: a combustion model
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.
Stochastic Systems Uncertainty Quantification and Propagation
Grigoriu, Mircea
2012-01-01
Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: · A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis · Probabilistic models for random variables an...
Compositional Modelling of Stochastic Hybrid Systems
Strubbe, S.N.
2005-01-01
In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete
Stochastic Modelling Of The Repairable System
Directory of Open Access Journals (Sweden)
Andrzejczak Karol
2015-11-01
Full Text Available All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.
Reaction-diffusion controlled growth of complex structures
Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna
2013-03-01
Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support
Integration of stochastic generation in power systems
Papaefthymiou, G.; Schavemaker, P.H.; Sluis, van der L.; Kling, W.L.; Kurowicka, D.; Cooke, R.M.
2006-01-01
Stochastic generation, i.e., electrical power production by an uncontrolled primary energy source, is expected to play an important role in future power systems. A new power system structure is created due to the large-scale implementation of this small-scale, distributed, non-dispatchable
Stochastic hybrid systems with renewal transitions
Guerreiro Tome Antunes, D.J.; Hespanha, J.P.; Silvestre, C.J.
2010-01-01
We consider Stochastic Hybrid Systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an analysis framework based on a set of Volterra renewal-type equations, which allows us to compute any statistical
Linear System Control Using Stochastic Learning Automata
Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.
1998-01-01
This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
The unsaturated bistable stochastic resonance system.
Zhao, Wenli; Wang, Juan; Wang, Linze
2013-09-01
We investigated the characteristics of the output saturation of the classical continuous bistable system (saturation bistable system) and its impact on stochastic resonance (SR). We further proposed a piecewise bistable SR system (unsaturated bistable system) and developed the expression of signal-to-noise ratio (SNR) using the adiabatic approximation theory. Compared with the saturation bistable system, the SNR is significantly improved in our unsaturated bistable SR system. The numerical simulation showed that the unsaturated bistable system performed better in extracting weak signals from strong background noise than the saturation bistable system.
Stochastic transport processes in discrete biological systems
Frehland, Eckart
1982-01-01
These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio logical 'transport systems can be complex. For example, the tr...
Stochastic cooling with a double rf system
International Nuclear Information System (INIS)
Wei, Jie.
1992-01-01
Stochastic cooling for a bunched beam of hadrons stored in an accelerator with a double rf system of two different frequencies has been investigated. The double rf system broadens the spread in synchrotron-oscillation frequency of the particles when they mostly oscillate near the center of the rf bucket. Compared with the ease of a single rf system, the reduction rates of the bunch dimensions are significantly increased. When the rf voltage is raised, the reduction rate, instead of decreasing linearly, now is independent of the ratio of the bunch area to the bucket area. On the other hand, the spread in synchrotron-oscillation frequency becomes small with the double rf system, if the longitudinal oscillation amplitudes of the particles are comparable to the dimension of the rf bucket. Consequently, stochastic cooling is less effective when the bunch area is close to the bucket area
Guiding brine shrimp through mazes by solving reaction diffusion equations
Singal, Krishma; Fenton, Flavio
Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.
Reaction-diffusion modeling of hydrogen in beryllium
Energy Technology Data Exchange (ETDEWEB)
Wensing, Mirko; Matveev, Dmitry; Linsmeier, Christian [Forschungszentrum Juelich GmbH, Institut fuer Energie- und Klimaforschung - Plasmaphysik (Germany)
2016-07-01
Beryllium will be used as first-wall material for the future fusion reactor ITER as well as in the breeding blanket of DEMO. In both cases it is important to understand the mechanisms of hydrogen retention in beryllium. In earlier experiments with beryllium low-energy binding states of hydrogen were observed by thermal desorption spectroscopy (TDS) which are not yet well understood. Two candidates for these states are considered: beryllium-hydride phases within the bulk and surface effects. The retention of deuterium in beryllium is studied by a reaction rate approach using a coupled reaction diffusion system (CRDS)-model relying on ab initio data from density functional theory calculations (DFT). In this contribution we try to assess the influence of surface recombination.
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Sinitsyn, Nikolai [Los Alamos National Laboratory
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Studies in the Control of Stochastic Systems
2017-10-31
control of continuous time stochastic systems with noise that is Brownian motions or fractional Brownian motions, the control of discrete time...in both continuous and discrete time. All of the above types of problems have been studied with the support of this grant. The achievement of these...scientists and engineers. 2. Math Awareness Months (MAM) (Every April for the past twenty-three years) Agenda: workshops each year for fifth
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
is that the model structure has to be adequate for practical applications, such as system simulation, fault detection and diagnosis, and design of control strategies. This also reflects on the methods used for identification of the component models. The main result from this research is the identification......In this thesis dynamic models of typical components in Danish heating systems are considered. Emphasis is made on describing and evaluating mathematical methods for identification of such models, and on presentation of component models for practical applications. The thesis consists of seven...... research papers (case studies) together with a summary report. Each case study takes it's starting point in typical heating system components and both, the applied mathematical modelling methods and the application aspects, are considered. The summary report gives an introduction to the scope...
Mathematical models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
International Nuclear Information System (INIS)
Li Zuoan; Li Kelin
2009-01-01
In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.
Lectures on Dynamics of Stochastic Systems
Klyatskin, Valery I
2010-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised a
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-01-01
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge
Field theory of propagating reaction-diffusion fronts
International Nuclear Information System (INIS)
Escudero, C.
2004-01-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations
Study of ODE limit problems for reaction-diffusion equations
Directory of Open Access Journals (Sweden)
Jacson Simsen
2018-01-01
Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.
The intrinsic stochasticity of near-integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu
1989-09-01
Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter; Taká č, Martin
2017-01-01
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter
2017-06-04
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
Dynamics of non-holonomic systems with stochastic transport
Holm, D. D.; Putkaradze, V.
2018-01-01
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.
System Entropy Measurement of Stochastic Partial Differential Systems
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Bor-Sen Chen
2016-03-01
Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.
Large-scale stochasticity in Hamiltonian systems
International Nuclear Information System (INIS)
Escande, D.F.
1982-01-01
Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)
Filtering and control of stochastic jump hybrid systems
Yao, Xiuming; Zheng, Wei Xing
2016-01-01
This book presents recent research work on stochastic jump hybrid systems. Specifically, the considered stochastic jump hybrid systems include Markovian jump Ito stochastic systems, Markovian jump linear-parameter-varying (LPV) systems, Markovian jump singular systems, Markovian jump two-dimensional (2-D) systems, and Markovian jump repeated scalar nonlinear systems. Some sufficient conditions are first established respectively for the stability and performances of those kinds of stochastic jump hybrid systems in terms of solution of linear matrix inequalities (LMIs). Based on the derived analysis conditions, the filtering and control problems are addressed. The book presents up-to-date research developments and novel methodologies on stochastic jump hybrid systems. The contents can be divided into two parts: the first part is focused on robust filter design problem, while the second part is put the emphasis on robust control problem. These methodologies provide a framework for stability and performance analy...
Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
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Alejandro Vázquez-Otero
2015-05-01
Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
Time-ordered product expansions for computational stochastic system biology
International Nuclear Information System (INIS)
Mjolsness, Eric
2013-01-01
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. (paper)
Stochastic resonance in a stochastic bistable system with additive noises and square–wave signal
International Nuclear Information System (INIS)
Feng, Guo; Xiang-Dong, Luo; Shao-Fu, Li; Yu-Rong, Zhou
2010-01-01
This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated. (general)
Computational singular perturbation analysis of stochastic chemical systems with stiffness
Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.
2017-04-01
Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.
Stochastic resonance in bistable systems driven by harmonic noise
International Nuclear Information System (INIS)
Neiman, A.; Schimansky-Geier, L.
1994-01-01
We study stochastic resonance in a bistable system which is excited simultaneously by white and harmonic noise which we understand as the signal. In our case the spectral line of the signal has a finite width as it occurs in many real situations. Using techniques of cumulant analysis as well as computer simulations we find that the effect of stochastic resonance is preserved in the case of harmonic noise excitation. Moreover we show that the width of the spectral line of the signal at the output can be decreased via stochastic resonance. The last could be of importance in the practical using of the stochastic resonance
Stochasticity and transport in Hamiltonian systems
International Nuclear Information System (INIS)
MacKay, R.S.; Meiss, J.D.; Percival, I.C.
1983-08-01
The theory of transport in nonlinear dynamics is developed in terms of leaky barriers which remain when invariant tori are destroyed. We describe the organization of stochastic motion by these barriers and give an explanation of long-time correlations in the stochastic regime
Stochastic equations for complex systems theoretical and computational topics
Bessaih, Hakima
2015-01-01
Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations ...
Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs
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Bernard Girau
2009-01-01
and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.
Stochastic stability of four-wheel-steering system
International Nuclear Information System (INIS)
Huang Dongwei; Wang Hongli; Zhu Zhiwen; Feng Zhang
2007-01-01
A four-wheel-steering system subjected to white noise excitations was reduced to a two-degree-of-freedom quasi-non-integrable-Hamiltonian system. Subsequently we obtained an one-dimensional Ito stochastic differential equation for the averaged Hamiltonian of the system by using the stochastic averaging method for quasi-non-integrable-Hamiltonian systems. Thus, the stochastic stability of four-wheel-steering system was analyzed by analyzing the sample behaviors of the averaged Hamiltonian at the boundary H = 0 and calculating its Lyapunov exponent. An example given at the end demonstrated that the conclusion obtained is of considerable significance
Process theory for supervisory control of stochastic systems with data
Markovski, J.
2012-01-01
We propose a process theory for supervisory control of stochastic nondeterministic plants with data-based observations. The Markovian process theory with data relies on the notion of Markovian partial bisimulation to capture controllability of stochastic nondeterministic systems. It presents a
Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson
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Bullinger Eric
2006-12-01
Full Text Available Abstract "Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.
Numerical analysis of systems of ordinary and stochastic differential equations
Artemiev, S S
1997-01-01
This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).
Formal Abstractions for Automated Verification and Synthesis of Stochastic Systems
Esmaeil Zadeh Soudjani, S.
2014-01-01
Stochastic hybrid systems involve the coupling of discrete, continuous, and probabilistic phenomena, in which the composition of continuous and discrete variables captures the behavior of physical systems interacting with digital, computational devices. Because of their versatility and generality,
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
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Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
Generalization of uncertainty relation for quantum and stochastic systems
Koide, T.; Kodama, T.
2018-06-01
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.
Event-triggered synchronization for reaction-diffusion complex networks via random sampling
Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng
2018-04-01
In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Desvillettes, Laurent; Fellner, Klemens
2008-01-01
In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
Distributed Fault Detection for a Class of Nonlinear Stochastic Systems
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Bingyong Yan
2014-01-01
Full Text Available A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs. Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.
Numerical solution of a reaction-diffusion equation
International Nuclear Information System (INIS)
Moyano, Edgardo A.; Scarpettini, Alberto F.
2000-01-01
The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
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Petr Stehlík
2015-01-01
Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.
Reaction time for trimolecular reactions in compartment-based reaction-diffusion models
Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang
2018-05-01
Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.
Attractor of reaction-diffusion equations in Banach spaces
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José Valero
2001-04-01
Full Text Available In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space Lp is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L2 are obtained.
Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts
Nefedov, Nikolay
2016-06-01
In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial boundary value problems. We present results on stability and on the motion of the fronts.
Reaction diffusion voronoi diagrams: from sensors data to computing
Czech Academy of Sciences Publication Activity Database
Vázquez-Otero, Alejandro (ed.); Faigl, J.; Dormido, R.; Duro, N.
2015-01-01
Roč. 15, č. 6 (2015), s. 12736-12764 ISSN 1424-8220 R&D Projects: GA MŠk ED1.1.00/02.0061 Grant - others:ELI Beamlines(XE) CZ.1.05/1.1.00/02.0061 Institutional support: RVO:68378271 Keywords : reaction diffusion * FitzHugh–Nagumo * path planning * navigation * exploration Subject RIV: BD - Theory of Information Impact factor: 2.033, year: 2015
A decoupled approach to filter design for stochastic systems
Barbata, A.; Zasadzinski, M.; Ali, H. Souley; Messaoud, H.
2016-08-01
This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.
Stochastic chemical kinetics theory and (mostly) systems biological applications
Érdi, Péter; Lente, Gabor
2014-01-01
This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.
Stochastic systems with cross-correlated Gaussian white noises
International Nuclear Information System (INIS)
Wang Cheng-Yu; Song Yu-Min; Zhou Peng; Yang Hai; Gao Yun
2010-01-01
This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the cross-correlated noises are studied. The stationary solutions of the Fokker—Planck equation for three specific examples are analysed. It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions
Stochastic bosonization for a d ≥ 3 Fermi system
International Nuclear Information System (INIS)
Accardi, L.; Lu, Y.G.; Mastropietro, V.
1997-01-01
We consider a system of fermions interacting via an external field and we prove, in d ≥ 3, that a suitable collective operator, bilinear in the fermionic fields, in the stochastic limit becomes a boson quantum brownian motion. The evolution operator after the limit satisfies a quantum stochastic differential equation, in which the imaginary part of the Ito correction is the ground state shift while its real part is the lifetime of the ground state. (orig.)
Stochastic differential equations and a biological system
DEFF Research Database (Denmark)
Wang, Chunyan
1994-01-01
The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based...... on experimental data is considered. As an example, the growth of bacteria Pseudomonas fluorescens is taken. Due to the specific features of stochastic differential equations, namely that their solutions do not exist in the general sense, two new integrals - the Ito integral and the Stratonovich integral - have...... description. In order to identify the parameters, a Maximum likelihood estimation method is used together with a simplified truncated second order filter. Because of the continuity feature of the predictor equation, two numerical integration methods, called the Odeint and the Discretization method...
Reaction-diffusion fronts with inhomogeneous initial conditions
Energy Technology Data Exchange (ETDEWEB)
Bena, I [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Martens, K [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest (Hungary)
2007-02-14
Properties of reaction zones resulting from A+B {yields} C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.
On the solutions of fractional reaction-diffusion equations
Directory of Open Access Journals (Sweden)
Jagdev Singh
2013-05-01
Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.
Explosive instabilities of reaction-diffusion equations including pinch effects
International Nuclear Information System (INIS)
Wilhelmsson, H.
1992-01-01
Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch and source processes certain 'bell-shaped' distributions may grow explosively in time with preserved shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or. more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma. (au) (18 refs.)
Distributed parallel computing in stochastic modeling of groundwater systems.
Dong, Yanhui; Li, Guomin; Xu, Haizhen
2013-03-01
Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.
Stochastic Sizing of Energy Storage Systems for Wind Integration
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D. D. Le
2018-06-01
Full Text Available In this paper, we present an optimal capacity decision model for energy storage systems (ESSs in combined operation with wind energy in power systems. We use a two-stage stochastic programming approach to take into account both wind and load uncertainties. The planning problem is formulated as an AC optimal power flow (OPF model with the objective of minimizing ESS installation cost and system operation cost. Stochastic wind and load inputs for the model are generated from historical data using clustering technique. The model is tested on the IEEE 39-bus system.
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua
2016-11-14
In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
Probabilistic DHP adaptive critic for nonlinear stochastic control systems.
Herzallah, Randa
2013-06-01
Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.
Hopf Bifurcation of Compound Stochastic van der Pol System
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Shaojuan Ma
2016-01-01
Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.
Optimal Control and Optimization of Stochastic Supply Chain Systems
Song, Dong-Ping
2013-01-01
Optimal Control and Optimization of Stochastic Supply Chain Systems examines its subject in the context of the presence of a variety of uncertainties. Numerous examples with intuitive illustrations and tables are provided, to demonstrate the structural characteristics of the optimal control policies in various stochastic supply chains and to show how to make use of these characteristics to construct easy-to-operate sub-optimal policies. In Part I, a general introduction to stochastic supply chain systems is provided. Analytical models for various stochastic supply chain systems are formulated and analysed in Part II. In Part III the structural knowledge of the optimal control policies obtained in Part II is utilized to construct easy-to-operate sub-optimal control policies for various stochastic supply chain systems accordingly. Finally, Part IV discusses the optimisation of threshold-type control policies and their robustness. A key feature of the book is its tying together of ...
Nonequilibrium statistical mechanics and stochastic thermodynamics of small systems
International Nuclear Information System (INIS)
Tu Zhanchun
2014-01-01
Thermodynamics is an old subject. The research objects in conventional thermodynamics are macroscopic systems with huge number of particles. In recent 30 years, thermodynamics of small systems is a frontier topic in physics. Here we introduce nonequilibrium statistical mechanics and stochastic thermodynamics of small systems. As a case study, we construct a Canot-like cycle of a stochastic heat engine with a single particle controlled by a time-dependent harmonic potential. We find that the efficiency at maximum power is 1 - √T c /T h , where Tc and Th are the temperatures of cold bath and hot bath, respectively. (author)
Size and stochasticity in irrigated social-ecological systems
Puy, Arnald; Muneepeerakul, Rachata; Balbo, Andrea L.
2017-03-01
This paper presents a systematic study of the relation between the size of irrigation systems and the management of uncertainty. We specifically focus on studying, through a stylized theoretical model, how stochasticity in water availability and taxation interacts with the stochastic behavior of the population within irrigation systems. Our results indicate the existence of two key population thresholds for the sustainability of any irrigation system: or the critical population size required to keep the irrigation system operative, and N* or the population threshold at which the incentive to work inside the irrigation system equals the incentives to work elsewhere. Crossing irretrievably leads to system collapse. N* is the population level with a sub-optimal per capita payoff towards which irrigation systems tend to gravitate. When subjected to strong stochasticity in water availability or taxation, irrigation systems might suffer sharp population drops and irreversibly disintegrate into a system collapse, via a mechanism we dub ‘collapse trap’. Our conceptual study establishes the basis for further work aiming at appraising the dynamics between size and stochasticity in irrigation systems, whose understanding is key for devising mitigation and adaptation measures to ensure their sustainability in the face of increasing and inevitable uncertainty.
Multi-scenario modelling of uncertainty in stochastic chemical systems
International Nuclear Information System (INIS)
Evans, R. David; Ricardez-Sandoval, Luis A.
2014-01-01
Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo
? filtering for stochastic systems driven by Poisson processes
Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya
2015-01-01
This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.
Stochastic responses of tumor–immune system with periodic treatment
International Nuclear Information System (INIS)
Li Dong-Xi; Li Ying
2017-01-01
We investigate the stochastic responses of a tumor–immune system competition model with environmental noise and periodic treatment. Firstly, a mathematical model describing the interaction between tumor cells and immune system under external fluctuations and periodic treatment is established based on the stochastic differential equation. Then, sufficient conditions for extinction and persistence of the tumor cells are derived by constructing Lyapunov functions and Ito’s formula. Finally, numerical simulations are introduced to illustrate and verify the results. The results of this work provide the theoretical basis for designing more effective and precise therapeutic strategies to eliminate cancer cells, especially for combining the immunotherapy and the traditional tools. (paper)
Ray and wave optics of integrable and stochastic systems
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1979-07-01
The generalization of WKB methods to more than one dimension is discussed in terms of the integrability or non-integrability of the geometrical optics (ray Hamiltonian) system derived in the short-wave approximation. In the two-dimensional case the ray trajectories are either regular or stochastic, and the qualitative differences between these types of motion are manifested in the characteristics of the spectra and eigenfunctions. These are examined for a model system which may be integrable or stochastic, depending on a single parameter
Stochastic simulation of off-shore oil terminal systems
International Nuclear Information System (INIS)
Frankel, E.G.; Oberle, J.
1991-01-01
To cope with the problem of uncertainty and conditionality in the planning, design, and operation of offshore oil transshipment terminal systems, a conditional stochastic simulation approach is presented. Examples are shown, using SLAM II, a computer simulation language based on GERT, a conditional stochastic network analysis methodology in which use of resources such as time and money are expressed by the moment generating function of the statistics of the resource requirements. Similarly each activity has an associated conditional probability of being performed and/or of requiring some of the resources. The terminal system is realistically represented by modelling the statistics of arrivals, loading and unloading times, uncertainties in costs and availabilities, etc
Introduction to modeling and analysis of stochastic systems
Kulkarni, V G
2011-01-01
This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany...
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
International Nuclear Information System (INIS)
Indekeu, Joseph O; Smets, Ruben
2017-01-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Threshold for extinction and survival in stochastic tumor immune system
Li, Dongxi; Cheng, Fangjuan
2017-10-01
This paper mainly investigates the stochastic character of tumor growth and extinction in the presence of immune response of a host organism. Firstly, the mathematical model describing the interaction and competition between the tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Then, the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells are derived by the rigorous theoretical proofs. Finally, stochastic simulation are taken to substantiate and illustrate the conclusion we have derived. The modeling results will be beneficial to understand to concept of immunoediting, and develop the cancer immunotherapy. Besides, our simple theoretical model can help to obtain new insight into the complexity of tumor growth.
Directory of Open Access Journals (Sweden)
Le Novère Nicolas
2010-03-01
Full Text Available Abstract Background Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes. Results Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time. Conclusions Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.
Deterministic Versus Stochastic Interpretation of Continuously Monitored Sewer Systems
DEFF Research Database (Denmark)
Harremoës, Poul; Carstensen, Niels Jacob
1994-01-01
An analysis has been made of the uncertainty of input parameters to deterministic models for sewer systems. The analysis reveals a very significant uncertainty, which can be decreased, but not eliminated and has to be considered for engineering application. Stochastic models have a potential for ...
Optimal adaptive control for a class of stochastic systems
Bagchi, Arunabha; Chen, Han-Fu
1995-01-01
We study linear-quadratic adaptive tracking problems for a special class of stochastic systems expressed in the state-space form. This is a long-standing problem in the control of aircraft flying through atmospheric turbulence. Using an ELS-based algorithm and introducing dither in the control law
Stochastic Predictive Control of Multi-Microgrid Systems
DEFF Research Database (Denmark)
Bazmohammadi, Najmeh; Tahsiri, Ahmadreza; Anvari-Moghaddam, Amjad
2018-01-01
This paper presents a stochastic predictive control algorithm for a number of microgrids connected to the same distribution system. Each microgrid includes a variety of distributed resources such as wind turbine, photo voltaic units, energy storage devices and loads. Considering the uncertainty...
Stochastic Robust Mathematical Programming Model for Power System Optimization
Energy Technology Data Exchange (ETDEWEB)
Liu, Cong; Changhyeok, Lee; Haoyong, Chen; Mehrotra, Sanjay
2016-01-01
This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.
Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.
Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M
2016-12-01
Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.
Stochastic modeling of wetland-groundwater systems
Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca
2018-02-01
Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.
Stochastic Model Predictive Control with Applications in Smart Energy Systems
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Edlund, Kristian; Mølbak, Tommy
2012-01-01
to cover more than 50% of the total consumption by 2050. Energy systems based on significant amounts of renewable energy sources are subject to uncertainties. To accommodate the need for model predictive control (MPC) of such systems, the effect of the stochastic effects on the constraints must...... study, we consider a system consisting of fuel-fired thermal power plants, wind farms and electric vehicles....
Stochastic Turing Patterns: Analysis of Compartment-Based Approaches
Cao, Yang; Erban, Radek
2014-01-01
© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.
Stochastic Turing Patterns: Analysis of Compartment-Based Approaches
Cao, Yang
2014-11-25
© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.
Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties
Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong
2018-03-01
This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.
International Nuclear Information System (INIS)
Moyano, Edgardo A.; Scarpettini, Alberto F.
2003-01-01
A semi linear model of weakly coupled parabolic p.d.e. with reaction-diffusion is investigated. The system describes fission gas transfer from grain interior of UO 2 to grain boundaries. The problem is studied in a bounded domain. Using the upper-lower solutions method, two monotone sequences for the finite differences equations are constructed. Reasons are mentioned that allow to affirm that in the proposed functional sector the algorithm converges to the unique solution of the differential system. (author)
Multivariable controller for discrete stochastic amplitude-constrained systems
Directory of Open Access Journals (Sweden)
Hannu T. Toivonen
1983-04-01
Full Text Available A sub-optimal multivariable controller for discrete stochastic amplitude-constrained systems is presented. In the approach the regulator structure is restricted to the class of linear saturated feedback laws. The stationary covariances of the controlled system are evaluated by approximating the stationary probability distribution of the state by a gaussian distribution. An algorithm for minimizing a quadratic loss function is given, and examples are presented to illustrate the performance of the sub-optimal controller.
Improved Stochastic Subspace System Identification for Structural Health Monitoring
Chang, Chia-Ming; Loh, Chin-Hsiung
2015-07-01
Structural health monitoring acquires structural information through numerous sensor measurements. Vibrational measurement data render the dynamic characteristics of structures to be extracted, in particular of the modal properties such as natural frequencies, damping, and mode shapes. The stochastic subspace system identification has been recognized as a power tool which can present a structure in the modal coordinates. To obtain qualitative identified data, this tool needs to spend computational expense on a large set of measurements. In study, a stochastic system identification framework is proposed to improve the efficiency and quality of the conventional stochastic subspace system identification. This framework includes 1) measured signal processing, 2) efficient space projection, 3) system order selection, and 4) modal property derivation. The measured signal processing employs the singular spectrum analysis algorithm to lower the noise components as well as to present a data set in a reduced dimension. The subspace is subsequently derived from the data set presented in a delayed coordinate. With the proposed order selection criteria, the number of structural modes is determined, resulting in the modal properties. This system identification framework is applied to a real-world bridge for exploring the feasibility in real-time applications. The results show that this improved system identification method significantly decreases computational time, while qualitative modal parameters are still attained.
Evolution of density profiles for reaction-diffusion processes
International Nuclear Information System (INIS)
Ondarza-Rovira, R.
1990-01-01
The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)
A fractional reaction-diffusion description of supply and demand
Benzaquen, Michael; Bouchaud, Jean-Philippe
2018-02-01
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB
Klingbeil, G.; Erban, R.; Giles, M.; Maini, P. K.
2011-01-01
Motivation: The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new
Accelerated maximum likelihood parameter estimation for stochastic biochemical systems
Directory of Open Access Journals (Sweden)
Daigle Bernie J
2012-05-01
Full Text Available Abstract Background A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs. MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. Results We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2: an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods
A Stochastic Operational Planning Model for Smart Power Systems
Directory of Open Access Journals (Sweden)
Sh. Jadid
2014-12-01
Full Text Available Smart Grids are result of utilizing novel technologies such as distributed energy resources, and communication technologies in power system to compensate some of its defects. Various power resources provide some benefits for operation domain however, power system operator should use a powerful methodology to manage them. Renewable resources and load add uncertainty to the problem. So, independent system operator should use a stochastic method to manage them. A Stochastic unit commitment is presented in this paper to schedule various power resources such as distributed generation units, conventional thermal generation units, wind and PV farms, and demand response resources. Demand response resources, interruptible loads, distributed generation units, and conventional thermal generation units are used to provide required reserve for compensating stochastic nature of various resources and loads. In the presented model, resources connected to distribution network can participate in wholesale market through aggregators. Moreover, a novel three-program model which can be used by aggregators is presented in this article. Loads and distributed generation can contract with aggregators by these programs. A three-bus test system and the IEEE RTS are used to illustrate usefulness of the presented model. The results show that ISO can manage the system effectively by using this model
International Nuclear Information System (INIS)
Han, Renji; Dai, Binxiang
2017-01-01
Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.
Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback
Al Noufaey, K. S.
2018-06-01
This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.
Estimation of Parameters in Mean-Reverting Stochastic Systems
Directory of Open Access Journals (Sweden)
Tianhai Tian
2014-01-01
Full Text Available Stochastic differential equation (SDE is a very important mathematical tool to describe complex systems in which noise plays an important role. SDE models have been widely used to study the dynamic properties of various nonlinear systems in biology, engineering, finance, and economics, as well as physical sciences. Since a SDE can generate unlimited numbers of trajectories, it is difficult to estimate model parameters based on experimental observations which may represent only one trajectory of the stochastic model. Although substantial research efforts have been made to develop effective methods, it is still a challenge to infer unknown parameters in SDE models from observations that may have large variations. Using an interest rate model as a test problem, in this work we use the Bayesian inference and Markov Chain Monte Carlo method to estimate unknown parameters in SDE models.
Stochastic Resonance in a System of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Krawiecki, A.
1999-01-01
Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Roessler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on-off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed. (author)
Information theory and stochastics for multiscale nonlinear systems
Majda, Andrew J; Grote, Marcus J
2005-01-01
This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...
Stochastic dynamics of a delayed bistable system with multiplicative noise
Energy Technology Data Exchange (ETDEWEB)
Dung, Nguyen Tien, E-mail: dung-nguyentien10@yahoo.com, E-mail: dungnt@fpt.edu.vn [Department of Mathematics, FPT University, No 8 Ton That Thuyet, My Dinh, Tu Liem, Hanoi (Viet Nam)
2014-05-15
In this paper we investigate the properties of a delayed bistable system under the effect of multiplicative noise. We first prove the existence and uniqueness of the positive solution and show that its moments are uniformly bounded. Then, we study stochastic dynamics of the solution in long time, the lower and upper bounds for the paths and an estimate for the average value are provided.
Frequency-difference-dependent stochastic resonance in neural systems
Guo, Daqing; Perc, Matjaž; Zhang, Yangsong; Xu, Peng; Yao, Dezhong
2017-08-01
Biological neurons receive multiple noisy oscillatory signals, and their dynamical response to the superposition of these signals is of fundamental importance for information processing in the brain. Here we study the response of neural systems to the weak envelope modulation signal, which is superimposed by two periodic signals with different frequencies. We show that stochastic resonance occurs at the beat frequency in neural systems at the single-neuron as well as the population level. The performance of this frequency-difference-dependent stochastic resonance is influenced by both the beat frequency and the two forcing frequencies. Compared to a single neuron, a population of neurons is more efficient in detecting the information carried by the weak envelope modulation signal at the beat frequency. Furthermore, an appropriate fine-tuning of the excitation-inhibition balance can further optimize the response of a neural ensemble to the superimposed signal. Our results thus introduce and provide insights into the generation and modulation mechanism of the frequency-difference-dependent stochastic resonance in neural systems.
Perturbation expansions of stochastic wavefunctions for open quantum systems
Ke, Yaling; Zhao, Yi
2017-11-01
Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.
Energy-Based Controller Design of Stochastic Magnetic Levitation System
Directory of Open Access Journals (Sweden)
Weiwei Sun
2017-01-01
Full Text Available This paper investigates the control problem of magnetic levitation system, in which velocity feedback signal is influenced by stochastic disturbance. Firstly, single-degree-freedom magnetic levitation is regarded as an energy-transform action device. From the view of energy-balance relation, the magnetic levitation system is transformed into port-controlled Hamiltonian system model. Next, based on the Hamiltonian structure, the control law of magnetic levitation system is designed by applying Lyapunov theory. Finally, the simulation verifies the correctness of the proposed results.
Quality control system response to stochastic growth of amyloid fibrils
DEFF Research Database (Denmark)
Pigolotti, S.; Lizana, L.; Sneppen, K.
2013-01-01
We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. Aggregate growth is contrasted by the cell quality control system, that attacks them at different stages of the growth process, with an efficiency...... that decreases with their size. Model parameters are estimated from experimental data. Two qualitatively different behaviors emerge: a homeostatic state, where the quality control system is stable and aggregates of large sizes are not formed, and an oscillatory state, where the quality control system...
Stochastic Prediction of Ventilation System Performance
DEFF Research Database (Denmark)
Haghighat, F.; Brohus, Henrik; Frier, Christian
The paper briefly reviews the existing techniques for predicting the airflow rate due to the random nature of forcing functions, e.g. wind speed. The effort is to establish the relationship between the statistics of the output of a system and the statistics of the random input variables and param......The paper briefly reviews the existing techniques for predicting the airflow rate due to the random nature of forcing functions, e.g. wind speed. The effort is to establish the relationship between the statistics of the output of a system and the statistics of the random input variables...
Phasing of Debuncher Stochastic Cooling Transverse Systems
International Nuclear Information System (INIS)
Pasquinelli, Ralph
2000-01-01
With the higher frequency of the cooling systems in the Debuncher, a modified method of making transfer functions has been developed for transverse systems. (Measuring of the momentum systems is unchanged.) Speed in making the measurements is critical, as the beam tends to decelerate due to vacuum lifetime. In the 4-8 GHz band, the harmonics in the Debuncher are 6,700 to 13,400 times the revolution frequency. Every Hertz change in revolution frequency is multiplied by this harmonic number and becomes a frequency measurement error, which is an appreciable percent of the momentum width of the beam. It was originally thought that a momentum cooling system would be phased first so that the beam could be kept from drifting in revolution frequency. As it turned out, the momentum cooling was so effective (even with the gain turned down) that the momentum width normalized to fo became less than one Hertz on the Schottky pickup. A beam this narrow requires very precise measurement of tune and revolution frequency. It was difficult to get repeatable results. For initial measuring of the transverse arrays, relative phase and delay is all that is required, so the measurement settings outlined below will suffice. Once all input and output arrays are phased, a more precise measurement of all pickups to all kickers can be done with more points and both upper and lower side bands, as in figure 1. Settings on the network analyzer were adjusted for maximum measurement speed. Data is not analyzed until a complete set of measurements is taken. Start and stop frequencies should be chosen to be just slightly wider than the band being measured. For transverse systems, select betatron USB for the measurement type. This will make the measurement two times faster. Select 101 for the number of points, sweep time of 5 seconds, IF bandwidth 30 Hz, averages = 1. It is important during the phasing to continually measure the revolution frequency and beam width of the beam for transverse systems
Quantum dynamics of classical stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Casati, G
1983-01-01
It is shown that one hand Quantum Mechanics introduces limitations to the manifestations of chaotic motion resulting, for the case of the periodically kicked rotator, in the limitation of energy growth; also, as it is confirmed by numerical experiments, phenomena like the exponential instability of orbits, inherent to strongly chaotic systems, are absent here and therefore Quantum Mechanics appear to be more stable and predictable than Classical Mechanics. On the other hand, we have seen that nonrecurrent behavior may arise in Quantum Systems and it is connected to the presence of singular continuous spectrum. We conjecture that the classical chaotic behavior is reflected, at least partially, in the nature of the spectrum and the singular-continuity of the latter may possess a self-similar structure typical of classical chaos.
Stochastic seismic floor response analysis method for various damping systems
International Nuclear Information System (INIS)
Kitada, Y.; Hattori, K.; Ogata, M.; Kanda, J.
1991-01-01
A study using the stochastic seismic response analysis method which is applicable for the estimation of floor response spectra is carried out. It is pointed out as a shortcoming in this stochastic seismic response analysis method, that the method tends to overestimate floor response spectra for low damping systems, e.g. 1% of the critical damping ratio. An investigation on the cause of the shortcoming is carried out and a number of improvements in this method were also made to the original method by taking correlation of successive peaks in a response time history into account. The application of the improved method to a typical BWR reactor building is carried out. The resultant floor response spectra are compared with those obtained by deterministic time history analysis. Floor response spectra estimated by the improved method consistently cover the response spectra obtained by the time history analysis for various damping ratios. (orig.)
Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods
Directory of Open Access Journals (Sweden)
Tetsuya Misawa
2010-01-01
Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
International Nuclear Information System (INIS)
Branicki, M.; Majda, A.J.
2013-01-01
Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum
Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane
Hu, Wenjie; Duan, Yueliang
2018-04-01
We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.
International Nuclear Information System (INIS)
Xu Rui; Chaplain, M.A.J.; Davidson, F.A.
2006-01-01
In this paper, we first investigate a stage-structured competitive model with time delays, harvesting, and nonlocal spatial effect. By using an iterative technique recently developed by Wu and Zou (Wu J, Zou X. Travelling wave fronts of reaction-diffusion systems with delay. J Dynam Differen Equat 2001;13:651-87), sufficient conditions are established for the existence of travelling front solution connecting the two boundary equilibria in the case when there is no positive equilibrium. The travelling wave front corresponds to an invasion by a stronger species which drives the weaker species to extinction. Secondly, we consider a stage-structured competitive model with time delays and nonlocal spatial effect when the domain is finite. We prove the global stability of each of the nonnegative equilibria and demonstrate that the more complex model studied here admits three possible long term behaviors: coexistence, bistability and dominance as is the case for the standard Lotka-Voltera competitive model
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
Energy Technology Data Exchange (ETDEWEB)
Veronese, S.V.; Othmer, H.G. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
This paper describes the implementation of a solver for systems of semi-linear parabolic partial differential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall effectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-diffusion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the efficiency and accuracy of the method are given here; the theoretical analysis will be presented.
Optimal Integration of Intermittent Renewables: A System LCOE Stochastic Approach
Directory of Open Access Journals (Sweden)
Carlo Lucheroni
2018-03-01
Full Text Available We propose a system level approach to value the impact on costs of the integration of intermittent renewable generation in a power system, based on expected breakeven cost and breakeven cost risk. To do this, we carefully reconsider the definition of Levelized Cost of Electricity (LCOE when extended to non-dispatchable generation, by examining extra costs and gains originated by the costly management of random power injections. We are thus lead to define a ‘system LCOE’ as a system dependent LCOE that takes properly into account intermittent generation. In order to include breakeven cost risk we further extend this deterministic approach to a stochastic setting, by introducing a ‘stochastic system LCOE’. This extension allows us to discuss the optimal integration of intermittent renewables from a broad, system level point of view. This paper thus aims to provide power producers and policy makers with a new methodological scheme, still based on the LCOE but which updates this valuation technique to current energy system configurations characterized by a large share of non-dispatchable production. Quantifying and optimizing the impact of intermittent renewables integration on power system costs, risk and CO 2 emissions, the proposed methodology can be used as powerful tool of analysis for assessing environmental and energy policies.
Considering inventory distributions in a stochastic periodic inventory routing system
Yadollahi, Ehsan; Aghezzaf, El-Houssaine
2017-07-01
Dealing with the stochasticity of parameters is one of the critical issues in business and industry nowadays. Supply chain planners have difficulties in forecasting stochastic parameters of a distribution system. Demand rates of customers during their lead time are one of these parameters. In addition, holding a huge level of inventory at the retailers is costly and inefficient. To cover the uncertainty of forecasting demand rates, researchers have proposed the usage of safety stock to avoid stock-out. However, finding the precise level of safety stock depends on forecasting the statistical distribution of demand rates and their variations in different settings among the planning horizon. In this paper the demand rate distributions and its parameters are taken into account for each time period in a stochastic periodic IRP. An analysis of the achieved statistical distribution of the inventory and safety stock level is provided to measure the effects of input parameters on the output indicators. Different values for coefficient of variation are applied to the customers' demand rate in the optimization model. The outcome of the deterministic equivalent model of SPIRP is simulated in form of an illustrative case.
On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.
Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances
Zhang, Weiwei; Meng, Xinzhu
2018-02-01
In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.
Maximum principle for a stochastic delayed system involving terminal state constraints.
Wen, Jiaqiang; Shi, Yufeng
2017-01-01
We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.
Stochastic Modelling and Optimization of Complex Infrastructure Systems
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In this paper it is shown that recent progress in stochastic modelling and optimization in combination with advanced computer systems has now made it possible to improve the design and the maintenance strategies for infrastructure systems. The paper concentrates on highway networks and single large...... bridges. united states has perhaps the largest highway networks in the world with more than 0.5 million highway bridges; see Chase, S.B. 1999. About 40% of these bridges are considered deficient and more than $50 billion is estimated needed to correct the deficiencies; see Roberts, J.E. 2001...
Stochastic analysis of residential micro combined heat and power system
DEFF Research Database (Denmark)
Karami, H.; Sanjari, M. J.; Gooi, H. B.
2017-01-01
In this paper the combined heat and power functionality of a fuel-cell in a residential hybrid energy system, including a battery, is studied. The demand uncertainties are modeled by investigating the stochastic load behavior by applying Monte Carlo simulation. The colonial competitive algorithm...... algorithm. The optimized scheduling of different energy resources is listed in an efficient look-up table for all time intervals. The effects of time of use and the battery efficiency and its size are investigated on the operating cost of the hybrid energy system. The results of this paper are expected...
Stochastic network optimization with application to communication and queueing systems
Neely, Michael
2010-01-01
This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are prov
Optimum gain and phase for stochastic cooling systems
International Nuclear Information System (INIS)
Meer, S. van der.
1984-01-01
A detailed analysis of optimum gain and phase adjustment in stochastic cooling systems reveals that the result is strongly influenced by the beam feedback effect and that for optimum performance the system phase should change appreciably across each Schottky band. It is shown that the performance is not greatly diminished if a constant phase is adopted instead. On the other hand, the effect of mixing between pick-up and kicker (which produces a phase change similar to the optimum one) is shown to be less perturbing than is usually assumed, provided that the absolute value of the gain is not too far from the optimum value. (orig.)
The stochastic-cooling system for COSY-Juelich
International Nuclear Information System (INIS)
Brittner, P.; Danzglock, R.; Hacker, H.U.; Maier, R.; Pfister, U.; Prasuhn, D.; Singer, H.; Spiess, W.; Stockhorst, H.
1991-01-01
The cooling in the Cooler Synchrotron COSY will work in the ranges: Band 1: 1 to 1.8 GHz, Band 2: 1.8 to 3 GHz. The system allows cooling in the energy range of 0.8 to 2.5 GeV. The stochastic-cooling system is under development. Cooling characteristics have been calculated. The tanks are similar to those of the CERN-AC. But the COSY parameters have required changes of the tank design. Active RF components have been developed for COSY. Measured results are presented
Sheng, Yin; Zhang, Hao; Zeng, Zhigang
2017-10-01
This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.
Stochastic Neural Field Theory and the System-Size Expansion
Bressloff, Paul C.
2010-01-01
We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N → ∞) we recover standard activity-based or voltage-based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N) can be truncated to form a closed system of equations for the first-and second-order moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean-field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately determine exponentially small transitions. © by SIAM.
Economic MPC for a linear stochastic system of energy units
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura
2016-01-01
This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers...... in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...
Approaching complexity by stochastic methods: From biological systems to turbulence
Energy Technology Data Exchange (ETDEWEB)
Friedrich, Rudolf [Institute for Theoretical Physics, University of Muenster, D-48149 Muenster (Germany); Peinke, Joachim [Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg (Germany); Sahimi, Muhammad [Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-1211 (United States); Reza Rahimi Tabar, M., E-mail: mohammed.r.rahimi.tabar@uni-oldenburg.de [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg (Germany); Fachbereich Physik, Universitaet Osnabrueck, Barbarastrasse 7, 49076 Osnabrueck (Germany)
2011-09-15
This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.
Approaching complexity by stochastic methods: From biological systems to turbulence
International Nuclear Information System (INIS)
Friedrich, Rudolf; Peinke, Joachim; Sahimi, Muhammad; Reza Rahimi Tabar, M.
2011-01-01
This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.
The stochastic system approach for estimating dynamic treatments effect.
Commenges, Daniel; Gégout-Petit, Anne
2015-10-01
The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.
Stochastic population dynamics in spatially extended predator-prey systems
Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.
2018-02-01
Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex
A stochastic killing system for biological containment of Escherichia coli
DEFF Research Database (Denmark)
Klemm, P.; Jensen, Lars Bogø; Molin, Søren
1995-01-01
Bacteria with a stochastic conditional lethal containment system have been constructed. The invertible switch promoter located upstream of the fimA gene from Escherichia coli was inserted as expression cassette in front of the Lethal gef gene deleted of its own natural promoter. The resulting...... fusion was placed on a plasmid and transformed to E. coli. The phenotype connected with the presence of such a plasmid was to reduce the population growth rate with increasing significance as the cell growth rate was reduced. In very fast growing cells, there was no measurable effect on growth rate. When...
Hitting probabilities for nonlinear systems of stochastic waves
Dalang, Robert C
2015-01-01
The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap
Assessing predictability of a hydrological stochastic-dynamical system
Gelfan, Alexander
2014-05-01
The water cycle includes the processes with different memory that creates potential for predictability of hydrological system based on separating its long and short memory components and conditioning long-term prediction on slower evolving components (similar to approaches in climate prediction). In the face of the Panta Rhei IAHS Decade questions, it is important to find a conceptual approach to classify hydrological system components with respect to their predictability, define predictable/unpredictable patterns, extend lead-time and improve reliability of hydrological predictions based on the predictable patterns. Representation of hydrological systems as the dynamical systems subjected to the effect of noise (stochastic-dynamical systems) provides possible tool for such conceptualization. A method has been proposed for assessing predictability of hydrological system caused by its sensitivity to both initial and boundary conditions. The predictability is defined through a procedure of convergence of pre-assigned probabilistic measure (e.g. variance) of the system state to stable value. The time interval of the convergence, that is the time interval during which the system losses memory about its initial state, defines limit of the system predictability. The proposed method was applied to assess predictability of soil moisture dynamics in the Nizhnedevitskaya experimental station (51.516N; 38.383E) located in the agricultural zone of the central European Russia. A stochastic-dynamical model combining a deterministic one-dimensional model of hydrothermal regime of soil with a stochastic model of meteorological inputs was developed. The deterministic model describes processes of coupled heat and moisture transfer through unfrozen/frozen soil and accounts for the influence of phase changes on water flow. The stochastic model produces time series of daily meteorological variables (precipitation, air temperature and humidity), whose statistical properties are similar
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Discrete changes of current statistics in periodically driven stochastic systems
International Nuclear Information System (INIS)
Chernyak, Vladimir Y; Sinitsyn, N A
2010-01-01
We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in the evolution of the moment generating function which is akin to the topological geometric phase in the evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd numbers of particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to this sign change should enclose specific degeneracy points in the space of control parameters. The relation between the topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel–Whitney class of topological invariants. (letter)
Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps
Yi, Taishan; Chen, Yuming
2017-12-01
In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.
Information Dynamics of a Nonlinear Stochastic Nanopore System
Directory of Open Access Journals (Sweden)
Claire Gilpin
2018-03-01
Full Text Available Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER and specific entropy rate (SER computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.
What can go wrong in stochastic cooling systems
AUTHOR|(CDS)2108502
2016-01-01
This paper discusses very practical aspects of stochastic cooling systems both during construction, running-in, operation and trouble shooting. Due to the high electronic gain, high sensitivity and large bandwidth of such systems, precautions have to be taken to avoid all sorts of EMI/EMC related problems as well as crosstalk and self-oscillations. Since un-intended beam heating is always much more efficient than the desired cooling the overall performance depends critically on avoiding this heating which often takes places outside the nominal frequency band of operation. Another important aspect is “cross heating”, i.e., unavoidable crosstalk from longitudinal to transverse systems and vice versa. Obviously adequate measurement procedures with beam for gain phase and optimum delay are mandatory and certain caveats and hints are given. The paper concludes with a listing of unusual and unexpected problems found during many years of operation of such systems at CERN.
A condition-based maintenance policy for stochastically deteriorating systems
International Nuclear Information System (INIS)
Grall, A.; Berenguer, C.; Dieulle, L.
2002-01-01
We focus on the analytical modeling of a condition-based inspection/replacement policy for a stochastically and continuously deteriorating single-unit system. We consider both the replacement threshold and the inspection schedule as decision variables for this maintenance problem and we propose to implement the maintenance policy using a multi-level control-limit rule. In order to assess the performance of the proposed maintenance policy and to minimize the long run expected maintenance cost per unit time, a mathematical model for the maintained system cost is derived, supported by the existence of a stationary law for the maintained system state. Numerical experiments illustrate the performance of the proposed policy and confirm that the maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the maintenance structure thresholds, or equivalently by a joint optimization of a system replacement threshold and the aperiodic inspection schedule
International Nuclear Information System (INIS)
Liang Jinling; Cao Jinde
2003-01-01
Employing general Halanay inequality, we analyze the global exponential stability of a class of reaction-diffusion recurrent neural networks with time-varying delays. Several new sufficient conditions are obtained to ensure existence, uniqueness and global exponential stability of the equilibrium point of delayed reaction-diffusion recurrent neural networks. The results extend and improve the earlier publications. In addition, an example is given to show the effectiveness of the obtained result
Quantization of dynamical systems and stochastic control theory
International Nuclear Information System (INIS)
Guerra, F.; Morato, L.M.
1982-09-01
In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior
A stochastic perturbation theory for non-autonomous systems
Energy Technology Data Exchange (ETDEWEB)
Moon, W., E-mail: wm275@damtp.cam.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Wettlaufer, J. S., E-mail: wettlaufer@maths.ox.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
2013-12-15
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.
Stochastic transport in complex systems from molecules to vehicles
Schadschneider, Andreas; Nishinari, Katsuhiro
2011-01-01
What is common between a motor protein, an ant and a vehicle? Each can be modelled as a"self-propelled particle"whose forward movement can be hindered by another in front of it. Traffic flow of such interacting driven"particles"has become an active area of interdisciplinary research involving physics, civil engineering and computer science. We present a unified pedagogical introduction to the analytical and computational methods which are currently used for studying such complex systems far from equilibrium. We also review a number of applications ranging from intra-cellular molecular motor transport in living systems to ant trails and vehicular traffic. Researchers working on complex systems, in general, and on classical stochastic transport, in particular, will find the pedagogical style, scholarly critical overview and extensive list of references extremely useful.
Erdal, Jørgen Sørgård
2017-01-01
This master thesis develops a stochastic optimisation software for household grid-connected batteries combined with PV-systems. The objective of the optimisation is to operate the battery system in order to minimise the costs of the consumer, and it was implemented in MATLAB using a self-written stochastic dynamic programming algorithm. Load was considered as a stochastic variable and modelled as a Markov Chain. Transition probabilities between time steps were calculated using historic load p...
Directory of Open Access Journals (Sweden)
Shaolin Ji
2013-01-01
Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
Nonlinear stochastic systems with incomplete information filtering and control
Shen, Bo; Shu, Huisheng
2013-01-01
Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: · a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; · new concepts such as random sensor and signal saturations for more realistic modeling; and · demonstration of the use of techniques such...
Stochastic Control Synthesis of Systems with Structured Uncertainty
Padula, Sharon L. (Technical Monitor); Crespo, Luis G.
2003-01-01
This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Stochastic linear hybrid systems: Modeling, estimation, and application
Seah, Chze Eng
Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS
Stochastic analysis of residential micro combined heat and power system
International Nuclear Information System (INIS)
Karami, H.; Sanjari, M.J.; Gooi, H.B.; Gharehpetian, G.B.; Guerrero, J.M.
2017-01-01
Highlights: • Applying colonial competitive algorithm to the problem of optimal dispatching. • Economic modeling of the residential integrated energy system. • Investigating differences of stand-alone and system-connected modes of fuel cell operation. • Considering uncertainty on the electrical load. • The effects of battery capacity and its efficiency on the system is investigated. - Abstract: In this paper the combined heat and power functionality of a fuel-cell in a residential hybrid energy system, including a battery, is studied. The demand uncertainties are modeled by investigating the stochastic load behavior by applying Monte Carlo simulation. The colonial competitive algorithm is adopted to the hybrid energy system scheduling problem and different energy resources are optimally scheduled to have optimal operating cost of hybrid energy system. In order to show the effectiveness of the colonial competitive algorithm, the results are compared with the results of the harmony search algorithm. The optimized scheduling of different energy resources is listed in an efficient look-up table for all time intervals. The effects of time of use and the battery efficiency and its size are investigated on the operating cost of the hybrid energy system. The results of this paper are expected to be used effectively in a real hybrid energy system.
Directory of Open Access Journals (Sweden)
Qiankun Song
2007-06-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Directory of Open Access Journals (Sweden)
Cao Jinde
2007-01-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Classical Solutions of Path-Dependent PDEs and Functional Forward-Backward Stochastic Systems
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Shaolin Ji
2013-01-01
Full Text Available In this paper we study the relationship between functional forward-backward stochastic systems and path-dependent PDEs. In the framework of functional Itô calculus, we introduce a path-dependent PDE and prove that its solution is uniquely determined by a functional forward-backward stochastic system.
Towards reaction-diffusion computing devices based on minority-carrier transport in semiconductors
International Nuclear Information System (INIS)
Asai, Tetsuya; Adamatzky, Andrew; Amemiya, Yoshihito
2004-01-01
Reaction-diffusion (RD) chemical systems are known to realize sensible computation when both data and results of the computation are encoded in concentration profiles of chemical species; the computation is implemented via spreading and interaction of either diffusive or phase waves. Thin-layer chemical systems are thought of therefore as massively-parallel locally-connected computing devices, where micro-volume of the medium is analogous to an elementary processor. Practical applications of the RD chemical systems are reduced however due to very low speed of traveling waves which makes real-time computation senseless. To overcome the speed-limitations while preserving unique features of RD computers we propose a semiconductor RD computing device where minority carriers diffuse as chemical species and reaction elements are represented by p-n-p-n diodes. We offer blue-prints of the RD semiconductor devices, and study in computer simulation propagation phenomena of the density wave of minority carriers. We then demonstrate what computational problems can be solved in RD semiconductor devices and evaluate space-time complexity of computation in the devices
Setting development goals using stochastic dynamical system models.
Ranganathan, Shyam; Nicolis, Stamatios C; Bali Swain, Ranjula; Sumpter, David J T
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers.
Online prediction and control in nonlinear stochastic systems
DEFF Research Database (Denmark)
Nielsen, Torben Skov
2002-01-01
speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...
Stochastic Petri net analysis of a replicated file system
Bechta Dugan, Joanne; Ciardo, Gianfranco
1989-01-01
A stochastic Petri-net model of a replicated file system is presented for a distributed environment where replicated files reside on different hosts and a voting algorithm is used to maintain consistency. Witnesses, which simply record the status of the file but contain no data, can be used in addition to or in place of files to reduce overhead. A model sufficiently detailed to include file status (current or out-of-date), as well as failure and repair of hosts where copies or witnesses reside, is presented. The number of copies and witnesses is a parameter of the model. Two different majority protocols are examined, one where a majority of all copies and witnesses is necessary to form a quorum, and the other where only a majority of the copies and witnesses on operational hosts is needed. The latter, known as adaptive voting, is shown to increase file availability in most cases.
Distinguishing signatures of determinism and stochasticity in spiking complex systems
Aragoneses, Andrés; Rubido, Nicolás; Tiana-Alsina, Jordi; Torrent, M. C.; Masoller, Cristina
2013-01-01
We describe a method to infer signatures of determinism and stochasticity in the sequence of apparently random intensity dropouts emitted by a semiconductor laser with optical feedback. The method uses ordinal time-series analysis to classify experimental data of inter-dropout-intervals (IDIs) in two categories that display statistically significant different features. Despite the apparent randomness of the dropout events, one IDI category is consistent with waiting times in a resting state until noise triggers a dropout, and the other is consistent with dropouts occurring during the return to the resting state, which have a clear deterministic component. The method we describe can be a powerful tool for inferring signatures of determinism in the dynamics of complex systems in noisy environments, at an event-level description of their dynamics.
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi
Computing the optimal path in stochastic dynamical systems
International Nuclear Information System (INIS)
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-01-01
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.
Systemic risk in dynamical networks with stochastic failure criterion
Podobnik, B.; Horvatic, D.; Bertella, M. A.; Feng, L.; Huang, X.; Li, B.
2014-06-01
Complex non-linear interactions between banks and assets we model by two time-dependent Erdős-Renyi network models where each node, representing a bank, can invest either to a single asset (model I) or multiple assets (model II). We use a dynamical network approach to evaluate the collective financial failure —systemic risk— quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided into sub-periods, where within each sub-period banks may contiguously fail due to links to either i) assets or ii) other banks, controlled by two parameters, probability of internal failure p and threshold Th (“solvency” parameter). The systemic risk decreases with the average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller Th), the smaller the systemic risk —for some Th values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic ii) controlled by probability p2 —a condition for the bank to be solvent (active) is stochastic— the systemic risk decreases with decreasing p2. We analyse the asset allocation for the U.S. banks.
Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion
Directory of Open Access Journals (Sweden)
Lei Zhang
2014-01-01
Full Text Available Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing, we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point (u2*,v2*,w2*, and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter c1, the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point (u1*,v1*,0, and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
Directory of Open Access Journals (Sweden)
Inci Cilingir Sungu
2015-01-01
Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.
Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture
Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong
The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.
International Nuclear Information System (INIS)
Caraballo, T.; Kloeden, P.E.
2006-01-01
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions. A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations. Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions
A stochastic approach for automatic generation of urban drainage systems.
Möderl, M; Butler, D; Rauch, W
2009-01-01
Typically, performance evaluation of new developed methodologies is based on one or more case studies. The investigation of multiple real world case studies is tedious and time consuming. Moreover extrapolating conclusions from individual investigations to a general basis is arguable and sometimes even wrong. In this article a stochastic approach is presented to evaluate new developed methodologies on a broader basis. For the approach the Matlab-tool "Case Study Generator" is developed which generates a variety of different virtual urban drainage systems automatically using boundary conditions e.g. length of urban drainage system, slope of catchment surface, etc. as input. The layout of the sewer system is based on an adapted Galton-Watson branching process. The sub catchments are allocated considering a digital terrain model. Sewer system components are designed according to standard values. In total, 10,000 different virtual case studies of urban drainage system are generated and simulated. Consequently, simulation results are evaluated using a performance indicator for surface flooding. Comparison between results of the virtual and two real world case studies indicates the promise of the method. The novelty of the approach is that it is possible to get more general conclusions in contrast to traditional evaluations with few case studies.
Stochastic Resource Allocation for Energy-Constrained Systems
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Sachs DanielGrobe
2009-01-01
Full Text Available Battery-powered wireless systems running media applications have tight constraints on energy, CPU, and network capacity, and therefore require the careful allocation of these limited resources to maximize the system's performance while avoiding resource overruns. Usually, resource-allocation problems are solved using standard knapsack-solving techniques. However, when allocating conservable resources like energy (which unlike CPU and network remain available for later use if they are not used immediately knapsack solutions suffer from excessive computational complexity, leading to the use of suboptimal heuristics. We show that use of Lagrangian optimization provides a fast, elegant, and, for convex problems, optimal solution to the allocation of energy across applications as they enter and leave the system, even if the exact sequence and timing of their entrances and exits is not known. This permits significant increases in achieved utility compared to heuristics in common use. As our framework requires only a stochastic description of future workloads, and not a full schedule, we also significantly expand the scope of systems that can be optimized.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Gan, Qintao; Lv, Tianshi; Fu, Zhenhua
2016-04-01
In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Semi-analytical stochastic analysis of the generalized van der Pol system
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
(2018) ISSN 1802-680X R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : stochastic stability * generalized van der Pol system * stochastic averaging * limit cycles Subject RIV: JM - Building Engineering OBOR OECD: Construction engineering, Municipal and structural engineering https://www.kme.zcu.cz/acm/acm/article/view/407
STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB
Klingbeil, G.
2011-02-25
Motivation: The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. Results: The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user\\'s models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. © The Author 2011. Published by Oxford University Press. All rights reserved.
Stochastic thermodynamics and entropy production of chemical reaction systems
Tomé, Tânia; de Oliveira, Mário J.
2018-06-01
We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end, we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states and on appropriate definitions of entropy and entropy production. The system is in contact with a heat reservoir and is placed out of equilibrium by the contact with particle reservoirs. In our approach, the fluxes of various types, such as the heat and particle fluxes, play a fundamental role in characterizing the nonequilibrium chemical state. We show that the rate of entropy production in the stationary nonequilibrium state is a bilinear form in the affinities and the fluxes of reaction, which are expressed in terms of rate constants and transition rates, respectively. We also show how the description in terms of microscopic states can be reduced to a description in terms of the numbers of particles of each species, from which follows the chemical master equation. As an example, we calculate the rate of entropy production of the first and second Schlögl reaction models.
A Buildings Module for the Stochastic Energy Deployment System
Energy Technology Data Exchange (ETDEWEB)
Lacommare, Kristina S H; Marnay, Chris; Stadler, Michael; Borgeson, Sam; Coffey, Brian; Komiyama, Ryoichi; Lai, Judy
2008-05-15
The U.S. Department of Energy (USDOE) is building a new long-range (to 2050) forecasting model for use in budgetary and management applications called the Stochastic Energy Deployment System (SEDS), which explicitly incorporates uncertainty through its development within the Analytica(R) platform of Lumina Decision Systems. SEDS is designed to be a fast running (a few minutes), user-friendly model that analysts can readily run and modify in its entirety through a visual programming interface. Lawrence Berkeley National Laboratory is responsible for implementing the SEDS Buildings Module. The initial Lite version of the module is complete and integrated with a shared code library for modeling demand-side technology choice developed by the National Renewable Energy Laboratory (NREL) and Lumina. The module covers both commercial and residential buildings at the U.S. national level using an econometric forecast of floorspace requirement and a model of building stock turnover as the basis for forecasting overall demand for building services. Although the module is fundamentally an engineering-economic model with technology adoption decisions based on cost and energy performance characteristics of competing technologies, it differs from standard energy forecasting models by including considerations of passive building systems, interactions between technologies (such as internal heat gains), and on-site power generation.
OPTIMAL TRAINING POLICY FOR PROMOTION - STOCHASTIC MODELS OF MANPOWER SYSTEMS
Directory of Open Access Journals (Sweden)
V.S.S. Yadavalli
2012-01-01
Full Text Available In this paper, the optimal planning of manpower training programmes in a manpower system with two grades is discussed. The planning of manpower training within a given organization involves a trade-off between training costs and expected return. These planning problems are examined through models that reflect the random nature of manpower movement in two grades. To be specific, the system consists of two grades, grade 1 and grade 2. Any number of persons in grade 2 can be sent for training and after the completion of training, they will stay in grade 2 and will be given promotion as and when vacancies arise in grade 1. Vacancies arise in grade 1 only by wastage. A person in grade 1 can leave the system with probability p. Vacancies are filled with persons in grade 2 who have completed the training. It is assumed that there is a perfect passing rate and that the sizes of both grades are fixed. Assuming that the planning horizon is finite and is T, the underlying stochastic process is identified as a finite state Markov chain and using dynamic programming, a policy is evolved to determine how many persons should be sent for training at any time k so as to minimize the total expected cost for the entire planning period T.
Fast cooling for a system of stochastic oscillators
Energy Technology Data Exchange (ETDEWEB)
Chen, Yongxin, E-mail: chen2468@umn.edu; Georgiou, Tryphon T., E-mail: tryphon@umn.edu [Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street S.E., Minneapolis, Minnesota 55455 (United States); Pavon, Michele, E-mail: pavon@math.unipd.it [Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova (Italy)
2015-11-15
We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired steady state corresponding to reduced thermal noise. Among the feedback controls achieving the desired asymptotic transfer, we find that the most efficient one from an energy point of view is characterized by time-reversibility. We also extend the theory of Schrödinger bridges to this model, thereby steering the system in finite time and with minimum effort to a target steady-state distribution. The system can then be maintained in this state through the optimal steady-state feedback control. The solution, in the finite-horizon case, involves a space-time harmonic function φ, and −logφ plays the role of an artificial, time-varying potential in which the desired evolution occurs. This framework appears extremely general and flexible and can be viewed as a considerable generalization of existing active control strategies such as macromolecular cooling. In the case of a quadratic potential, the results assume a form particularly attractive from the algorithmic viewpoint as the optimal control can be computed via deterministic matricial differential equations. An example involving inertial particles illustrates both transient and steady state optimal feedback control.
Stochastic and Macroscopic Thermodynamics of Strongly Coupled Systems
Directory of Open Access Journals (Sweden)
Christopher Jarzynski
2017-01-01
Full Text Available We develop a thermodynamic framework that describes a classical system of interest S that is strongly coupled to its thermal environment E. Within this framework, seven key thermodynamic quantities—internal energy, entropy, volume, enthalpy, Gibbs free energy, heat, and work—are defined microscopically. These quantities obey thermodynamic relations including both the first and second law, and they satisfy nonequilibrium fluctuation theorems. We additionally impose a macroscopic consistency condition: When S is large, the quantities defined within our framework scale up to their macroscopic counterparts. By satisfying this condition, we demonstrate that a unifying framework can be developed, which encompasses both stochastic thermodynamics at one end, and macroscopic thermodynamics at the other. A central element in our approach is a thermodynamic definition of the volume of the system of interest, which converges to the usual geometric definition when S is large. We also sketch an alternative framework that satisfies the same consistency conditions. The dynamics of the system and environment are modeled using Hamilton’s equations in the full phase space.
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
International Nuclear Information System (INIS)
Wang Jian; Lu Junguo
2008-01-01
In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits
WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism
Sick, Stefanie; Reinker, Stefan; Timmer, Jens; Schlake, Thomas
2006-12-01
Mathematical reaction-diffusion models have been suggested to describe formation of animal pigmentation patterns and distribution of epidermal appendages. However, the crucial signals and in vivo mechanisms are still elusive. Here we identify WNT and its inhibitor DKK as primary determinants of murine hair follicle spacing, using a combined experimental and computational modeling approach. Transgenic DKK overexpression reduces overall appendage density. Moderate suppression of endogenous WNT signaling forces follicles to form clusters during an otherwise normal morphogenetic program. These results confirm predictions of a WNT/DKK-specific mathematical model and provide in vivo corroboration of the reaction-diffusion mechanism for epidermal appendage formation.
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
Unlike traditional fossil-fuel based power generation, renewable generation such as wind power relies on uncontrollable prime sources such as wind speed. Wind speed varies stochastically, which to a large extent determines the stochastic behavior of power generation from wind farms...... that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal...
Control of stochastic resonance in bistable systems by using periodic signals
International Nuclear Information System (INIS)
Min, Lin; Li-Min, Fang; Yong-Jun, Zheng
2009-01-01
According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal. Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization. By adding a bistable system with a controllable periodic signal, fluctuations in the single potential well can be effectively controlled, thus affecting the probability transitions between the two potential wells. In this way, an effective control can be achieved which allows one to either enhance or realize stochastic resonance
International Nuclear Information System (INIS)
Hong, H.P.; Zhou, W.; Zhang, S.; Ye, W.
2014-01-01
Components in engineered systems are subjected to stochastic deterioration due to the operating environmental conditions, and the uncertainty in material properties. The components need to be inspected and possibly replaced based on preventive or failure replacement criteria to provide the intended and safe operation of the system. In the present study, we investigate the influence of dependent stochastic degradation of multiple components on the optimal maintenance decisions. We use copula to model the dependent stochastic degradation of components, and formulate the optimal decision problem based on the minimum expected cost rule and the stochastic dominance rules. The latter is used to cope with decision maker's risk attitude. We illustrate the developed probabilistic analysis approach and the influence of the dependency of the stochastic degradation on the preferred decisions through numerical examples
Stochastic assessment of investment efficiency in a power system
International Nuclear Information System (INIS)
Davidov, Sreten; Pantoš, Miloš
2017-01-01
The assessment of investment efficiency plays a critical role in investment prioritization in the context of electrical network expansion planning. Hence, this paper proposes new criteria for the cost-efficiency investment applied in the investment ranking process in electrical network planning, based on the assessment of the new investment candidates impact on active-power losses, bus voltages and line loadings in the network. These three general criteria are chosen due to their strong economic influence when the active-power losses and line loadings are considered and due to their significant impact on quality of supply allowed for the voltage profile. Electrical network reliability of supply is not addressed, since, this criterion has already been extensively applied in other solutions regarding investment efficiency assessment. The proposed ranking procedure involves a stochastic approach applying the Monte Carlo method in the scenario preparation. The number of scenarios is further reduced by the K-MEANS procedure in order to speed up the investment efficiency assessment. The proposed ranking procedure is tested using the standard New England test system. The results show that based on the newly involved investment assessment criteria indices, system operators will obtain a prioritized list of investments that will prevent excessive and economically wasteful spending. - Highlights: • Active-Power Loss Investment Efficiency Index LEI. • Voltage Profile Investment Efficiency Index VEI. • Active-Power Flow Loading Mitigation Investment Efficiency Index PEI. • Optimization model for network expansion planning with new indices.
Stochastic theory for classical and quantum mechanical systems
International Nuclear Information System (INIS)
Pena, L. de la; Cetto, A.M.
1975-01-01
From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section
MONTE CARLO SIMULATION OF MULTIFOCAL STOCHASTIC SCANNING SYSTEM
Directory of Open Access Journals (Sweden)
LIXIN LIU
2014-01-01
Full Text Available Multifocal multiphoton microscopy (MMM has greatly improved the utilization of excitation light and imaging speed due to parallel multiphoton excitation of the samples and simultaneous detection of the signals, which allows it to perform three-dimensional fast fluorescence imaging. Stochastic scanning can provide continuous, uniform and high-speed excitation of the sample, which makes it a suitable scanning scheme for MMM. In this paper, the graphical programming language — LabVIEW is used to achieve stochastic scanning of the two-dimensional galvo scanners by using white noise signals to control the x and y mirrors independently. Moreover, the stochastic scanning process is simulated by using Monte Carlo method. Our results show that MMM can avoid oversampling or subsampling in the scanning area and meet the requirements of uniform sampling by stochastically scanning the individual units of the N × N foci array. Therefore, continuous and uniform scanning in the whole field of view is implemented.
Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays
Directory of Open Access Journals (Sweden)
Manlika Rajchakit
2012-01-01
Full Text Available This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China)
2015-12-15
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
Modeling and Analysis of Networked Control Systems Using Stochastic Hybrid Systems
2014-09-03
The stability notions considered can be classified in two broad categories: bounds on the probability that the state of the system “ misbehaves ” or...alternative types of condi- tions: One is focused on making sure that the probability that the stochastic process “ misbehaves ” is very small. Such
Flexible single molecule simulation of reaction-diffusion processes
International Nuclear Information System (INIS)
Hellander, Stefan; Loetstedt, Per
2011-01-01
An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.
Scheduling of Power System Cells Integrating Stochastic Power Generation
International Nuclear Information System (INIS)
Costa, L.M.
2008-12-01
Energy supply and climate change are nowadays two of the most outstanding problems which societies have to cope with under a context of increasing energy needs. Public awareness of these problems is driving political willingness to take actions for tackling them in a swift and efficient manner. Such actions mainly focus in increasing energy efficiency, in decreasing dependence on fossil fuels, and in reducing greenhouse gas emissions. In this context, power systems are undergoing important changes in the way they are planned and managed. On the one hand, vertically integrated structures are being replaced by market structures in which power systems are un-bundled. On the other, power systems that once relied on large power generation facilities are witnessing the end of these facilities' life-cycle and, consequently, their decommissioning. The role of distributed energy resources such as wind and solar power generators is becoming increasingly important in this context. However, the large-scale integration of such type of generation presents many challenges due, for instance, to the uncertainty associated to the variability of their production. Nevertheless, advanced forecasting tools may be combined with more controllable elements such as energy storage devices, gas turbines, and controllable loads to form systems that aim to reduce the impacts that may be caused by these uncertainties. This thesis addresses the management under market conditions of these types of systems that act like independent societies and which are herewith named power system cells. From the available literature, a unified view of power system scheduling problems is also proposed as a first step for managing sets of power system cells in a multi-cell management framework. Then, methodologies for performing the optimal day-ahead scheduling of single power system cells are proposed, discussed and evaluated under both a deterministic and a stochastic framework that directly integrates the
Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.
Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan
2018-05-30
Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching.
Wu, Xiaotai; Tang, Yang; Cao, Jinde; Zhang, Wenbing
2016-08-01
In this paper, the distributed exponential consensus of stochastic delayed multi-agent systems with nonlinear dynamics is investigated under asynchronous switching. The asynchronous switching considered here is to account for the time of identifying the active modes of multi-agent systems. After receipt of confirmation of mode's switching, the matched controller can be applied, which means that the switching time of the matched controller in each node usually lags behind that of system switching. In order to handle the coexistence of switched signals and stochastic disturbances, a comparison principle of stochastic switched delayed systems is first proved. By means of this extended comparison principle, several easy to verified conditions for the existence of an asynchronously switched distributed controller are derived such that stochastic delayed multi-agent systems with asynchronous switching and nonlinear dynamics can achieve global exponential consensus. Two examples are given to illustrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
S. Aberkane
2007-01-01
Full Text Available This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI process. The specifications and objectives under consideration include stochastic stability, ℋ2 and ℋ∞ (or more generally, stochastic integral quadratic constraints performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.
Stochastic bounded consensus of second-order multi-agent systems in noisy environment
International Nuclear Information System (INIS)
Ren Hong-Wei; Deng Fei-Qi
2017-01-01
This paper investigates the stochastic bounded consensus of leader-following second-order multi-agent systems in a noisy environment. It is assumed that each agent received the information of its neighbors corrupted by noises and time delays. Based on the graph theory, stochastic tools, and the Lyapunov function method, we derive the sufficient conditions under which the systems would reach stochastic bounded consensus in mean square with the protocol we designed. Finally, a numerical simulation is illustrated to check the effectiveness of the proposed algorithms. (paper)
International Nuclear Information System (INIS)
Kostic, Lj.
2003-01-01
The influence of the stochastically pulsed Poisson source to the statistical properties of the subcritical multiplying system is analyzed in the paper. It is shown a strong dependence on the pulse period and pulse width of the source (author)
A constrained approach to multiscale stochastic simulation of chemically reacting systems
Cotter, Simon L.; Zygalakis, Konstantinos C.; Kevrekidis, Ioannis G.; Erban, Radek
2011-01-01
Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address
Witte, L.
2014-06-01
To support landing site assessments for HDA-capable flight systems and to facilitate trade studies between the potential HDA architectures versus the yielded probability of safe landing a stochastic landing dispersion model has been developed.
Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps
Wei, Yongchang; Yang, Qigui
2018-06-01
This paper is devoted to discern long time dynamics through the stochastic low concentration trimolecular oscillatory chemical system with jumps. By Lyapunov technique, this system is proved to have a unique global positive solution, and the asymptotic stability in mean square of such model is further established. Moreover, the existence of random attractor and Lyapunov exponents are obtained for the stochastic homeomorphism flow generated by the corresponding global positive solution. And some numerical simulations are given to illustrate the presented results.
Studies to the stochastic theory of coupled reactorkinetic-thermohydraulic systems Pt. 2
International Nuclear Information System (INIS)
Mesko, L.
1983-06-01
The description is given of the noise phenomena taking place in a multivariable coupled system by a comprehensive model based on the theory of stochastic fluctuations. A comparison is made with models using transfer function formalism for systems characterized by deterministic open and closed loop signal transmission properties. The advantages of the stochastic model are illustrated by simple reactor dynamical examples having diagnostical importance. (author)
Hu, Jun; Gao, Huijun
2014-01-01
This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties.The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects
Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
Composite system reliability evaluation by stochastic calculation of system operation
Energy Technology Data Exchange (ETDEWEB)
Haubrick, H -J; Hinz, H -J; Landeck, E [Dept. of Power Systems and Power Economics (Germany)
1994-12-31
This report describes a new developed probabilistic approach for steady-state composite system reliability evaluation and its exemplary application to a bulk power test system. The new computer program called PHOENIX takes into consideration transmission limitations, outages of lines and power stations and, as a central element, a highly sophisticated model to the dispatcher performing remedial actions after disturbances. The kernel of the new method is a procedure for optimal power flow calculation that has been specially adapted for the use in reliability evaluations under the above mentioned conditions. (author) 11 refs., 8 figs., 1 tab.
A reaction-diffusion model of CO2 influx into an oocyte
Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela
2012-01-01
We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674
Stochastic programming and market equilibrium analysis of microgrids energy management systems
International Nuclear Information System (INIS)
Hu, Ming-Che; Lu, Su-Ying; Chen, Yen-Haw
2016-01-01
Microgrids facilitate optimum utilization of distributed renewable energy, provides better local energy supply, and reduces transmission loss and greenhouse gas emission. Because the uncertainty in energy demand affects the energy demand and supply system, the aim of this research is to develop a stochastic optimization and its market equilibrium for microgrids in the electricity market. Therefore, a two-stage stochastic programming model for microgrids and the market competition model are derived in this paper. In the stochastic model, energy demand and supply uncertainties are considered. Furthermore, a case study of the stochastic model is conducted to simulate the uncertainties on the INER microgrids in Taiwanese market. The optimal investment of the generators and batteries installation and operating strategies are determined under energy demand and supply uncertainties for the INER microgrids. The results show optimal investment and operating strategies for the current INER microgrids are also determined by the proposed two-stage stochastic model in the market. In addition, trade-off between the battery capacity and microgrids performance is investigated. Battery usage and power trading between the microgrids and main grid systems are the functions of battery capacity. - Highlights: • A two-stage stochastic programming model is developed for microgrids. • Market equilibrium analysis of microgrids is conducted. • A case study of the stochastic model is conducted for INER microgrids.
International Nuclear Information System (INIS)
Song Lina; Zhang Hongqing
2007-01-01
In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.
Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
Optically levitated nanoparticle as a model system for stochastic bistable dynamics.
Ricci, F; Rica, R A; Spasenović, M; Gieseler, J; Rondin, L; Novotny, L; Quidant, R
2017-05-09
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.
Stamova, Ivanka; Stamov, Gani
2017-12-01
In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.
Speeding up stochastic analysis of bulk water supply systems using ...
African Journals Online (AJOL)
2013-10-22
Oct 22, 2013 ... It is possible to analyse the reliability of municipal storage tanks through stochastic analysis, in which the user demand, fire water demand and pipe failures are simulated using Monte Carlo analysis. While this technique could in principle be used to find the optimal size of a municipal storage tank, ...
Speeding up stochastic analysis of bulk water supply systems using ...
African Journals Online (AJOL)
It is possible to analyse the reliability of municipal storage tanks through stochastic analysis, in which the user demand, fire water demand and pipe failures are simulated using Monte Carlo analysis. While this technique could in principle be used to find the optimal size of a municipal storage tank, in practice the high ...
Directory of Open Access Journals (Sweden)
Dongping Wei
2015-01-01
Full Text Available Management of ecological tourism in protected areas faces many challenges, with visitation-related resource degradations and cultural impacts being two of them. To address those issues, several strategies including regulations, site managements, and visitor education programs have been commonly used in China and other countries. This paper presents a multiparameter stochastic differential equation model of an Ecological Tourism System to study how the populations of stakeholders vary in a finite time. The solution of Ordinary Differential Equation of Ecological Tourism System reveals that the system collapses when there is a lack of visitor educational intervention. Hence, the Stochastic Dynamic of Ecological Tourism System is introduced to suppress the explosion of the system. But the simulation results of the Stochastic Dynamic of Ecological Tourism System show that the system is still unstable and chaos in some small time interval. The Multiparameters Stochastic Dynamics of Ecological Tourism System is proposed to improve the performance in this paper. The Multiparameters Stochastic Dynamics of Ecological Tourism System not only suppresses the explosion of the system in a finite time, but also keeps the populations of stakeholders in an acceptable level. In conclusion, the Ecological Tourism System develops steadily and sustainably when land managers employ effective visitor education intervention programs to deal with recreation impacts.
On square-wave-driven stochastic resonance for energy harvesting in a bistable system
Energy Technology Data Exchange (ETDEWEB)
Su, Dongxu, E-mail: sudx@iis.u-tokyo.ac.jp [Graduate School of Engineering, The University of Tokyo, Tokyo 1538505 (Japan); Zheng, Rencheng; Nakano, Kimihiko [Institute of Industrial Science, The University of Tokyo, Tokyo 1538505 (Japan); Cartmell, Matthew P [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)
2014-11-15
Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation.
On square-wave-driven stochastic resonance for energy harvesting in a bistable system
International Nuclear Information System (INIS)
Su, Dongxu; Zheng, Rencheng; Nakano, Kimihiko; Cartmell, Matthew P
2014-01-01
Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation
Event-Triggered Faults Tolerant Control for Stochastic Systems with Time Delays
Directory of Open Access Journals (Sweden)
Ling Huang
2016-01-01
Full Text Available This paper is concerned with the state-feedback controller design for stochastic networked control systems (NCSs with random actuator failures and transmission delays. Firstly, an event-triggered scheme is introduced to optimize the performance of the stochastic NCSs. Secondly, stochastic NCSs under event-triggered scheme are modeled as stochastic time-delay systems. Thirdly, some less conservative delay-dependent stability criteria in terms of linear matrix inequalities for the codesign of both the controller gain and the trigger parameters are obtained by using delay-decomposition technique and convex combination approach. Finally, a numerical example is provided to show the less sampled data transmission and less conservatism of the proposed theory.
Stochastic resonance in a periodic potential system under a constant force
International Nuclear Information System (INIS)
Hu Gang.
1992-10-01
An overdamped particle moving in a periodic potential, and subject to a constant force and a stochastic force (i.e., χ = -sin(2πχ) + B + Γ(t),Γ(t) is a white noise) is considered. The mobility of the particle, d /dt, is investigated. The stochastic resonance type of behaviour is revealed. The study of the SR problem can thus be extended to systems with periodic force. (author). 13 refs
Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems
Directory of Open Access Journals (Sweden)
Hossein Shokouhi-Nejad
2014-01-01
Full Text Available This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin
2012-01-01
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.
Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective
Energy Technology Data Exchange (ETDEWEB)
Wang, Hong [Pacific Northwest National Laboratory (PNNL); Aziz, H M Abdul [ORNL; Young, Stan [National Renewable Energy Laboratory (NREL); Patil, Sagar [Pacific Northwest National Laboratory (PNNL)
2017-10-01
Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections. In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio
2015-09-01
A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.
Liu, Bingchen; Dong, Mengzhen; Li, Fengjie
2018-04-01
This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.
Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
International Nuclear Information System (INIS)
Armesto, Nestor; Bondarenko, Sergey; Quiroga-Arias, Paloma; Milhano, Jose Guilherme
2008-01-01
We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined-Reggeon Field Theory, Directed Percolation and Reversible Processes-only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.
Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients
Directory of Open Access Journals (Sweden)
Nauman Raza
2013-01-01
Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.
Liu, Ping; Shi, Junping
2018-01-01
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.
An analytic algorithm for the space-time fractional reaction-diffusion equation
Directory of Open Access Journals (Sweden)
M. G. Brikaa
2015-11-01
Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.
Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions
Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong
2013-08-01
This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.
International Nuclear Information System (INIS)
Lou, X.; Cui, B.
2008-01-01
In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)
A minimally-resolved immersed boundary model for reaction-diffusion problems
Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A
2013-01-01
We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...
A Stochastic Maximum Principle for General Mean-Field Systems
International Nuclear Information System (INIS)
Buckdahn, Rainer; Li, Juan; Ma, Jin
2016-01-01
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Basic aspects of stochastic reliability analysis for redundancy systems
International Nuclear Information System (INIS)
Doerre, P.
1989-01-01
Much confusion has been created by trying to establish common cause failure (CCF) as an extra phenomenon which has to be treated with extra methods in reliability and data analysis. This paper takes another approach which can be roughly described by the statement that dependent failure is the basic phenomenon, while 'independent failure' refers to a special limiting case, namely the perfectly homogeneous population. This approach is motivated by examples demonstrating that common causes do not lead to dependent failure, so far as physical dependencies like shared components are excluded, and that stochastic dependencies are not related to common causes. The possibility to select more than one failure behaviour from an inhomogeneous population is identified as an additional random process which creates stochastic dependence. However, this source of randomness is usually treated in the deterministic limit, which destroys dependence and hence yields incorrect multiple failure frequencies for redundancy structures, thus creating the need for applying corrective CCF models. (author)
A Stochastic Maximum Principle for General Mean-Field Systems
Energy Technology Data Exchange (ETDEWEB)
Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)
2016-12-15
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Contribution to an effective design method for stationary reaction-diffusion patterns
Energy Technology Data Exchange (ETDEWEB)
Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)
2015-06-15
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Contribution to an effective design method for stationary reaction-diffusion patterns
International Nuclear Information System (INIS)
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-01-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences
Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue
2018-01-01
This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.
Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue
2018-06-01
This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.
Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator
González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo
2018-05-01
We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.
Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal
International Nuclear Information System (INIS)
Yong-Feng, Guo; Wei, Xu; Liang, Wang
2010-01-01
This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker–Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time τ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears. (general)
Owolabi, Kolade M.
2018-03-01
In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.
Microscopic description of nuclear few-body systems with the stochastic variational method
International Nuclear Information System (INIS)
Suzuki, Yasuyuki
2000-01-01
A simple gambling procedure called the stochastic variational method can be applied, together with appropriate variational trial functions, to solve a few-body system where the correlation between the constituents plays an important role in determining its structure. The usefulness of the method is tested by comparing to other accurate solutions for Coulombic systems. Examples of application shown here include few-nucleon systems interacting with realistic forces and few-cluster systems with the Pauli principle being taken into account properly. These examples confirm the power of the stochastic variational method. There still remain many problems for extending to a system consisting of more particles. (author)
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.
2018-05-01
As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.
Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor
International Nuclear Information System (INIS)
Saha Ray, S.
2012-01-01
Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.
Directory of Open Access Journals (Sweden)
Jianxu Zhou
2018-03-01
Full Text Available Hydraulic vibration exists in various water conveyance projects and has resulted in different operating problems, but its obvious effects on system’s pressure head and stable operation have not been definitively addressed in the issued codes for engineering design, especially considering the uncertainties of hydraulic vibration. After detailed analysis of the randomness in hydraulic vibration and the commonly used stochastic approaches, in the basic equations for hydraulic vibration analysis, the random parameters and the formed stochastic equations were discussed for further probabilistic characteristic analysis of the random variables. Furthermore, preliminary investigation of the stochastic analysis of hydraulic vibration in pressurized pipelines and possible self-excited vibration in pumped-storage systems was presented for further consideration. The detailed discussion indicates that it is necessary to conduct further and systematic stochastic analysis of hydraulic vibration. Further, with the obtained frequencies and amplitudes in the form of a probability statement, the stochastic characteristics of various hydraulic vibrations can be investigated in detail and these solutions will be more reasonable for practical applications. Eventually, the stochastic analysis of hydraulic vibration will provide a basic premise to introduce its effect into the engineering design of water diversion and hydropower systems.
On the Use of Information Quality in Stochastic Networked Control Systems
DEFF Research Database (Denmark)
Olsen, Rasmus Løvenstein; Madsen, Jacob Theilgaard; Rasmussen, Jakob Gulddahl
2017-01-01
Networked control is challenged by stochastic delays that are caused by the communication networks as well as by the approach taken to exchange information about system state and set-points. Combined with stochastic changing information, there is a probability that information at the controller....... This is first analyzed in simulation models for the example system of a wind-farm controller. As simulation analysis is subject to stochastic variability and requires large computational effort, the paper develops a Markov model of a simplified networked control system and uses numerical results from the Markov...... is not matching the true system observation, which we call mismatch probability (mmPr). The hypothesis is that the optimization of certain parameters of networked control systems targeting mmPr is equivalent to the optimization targeting control performance, while the former is practically much easier to conduct...
de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás
2017-12-01
The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of
Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion
International Nuclear Information System (INIS)
Garrido-Atienza, Maria J.; Kloeden, Peter E.; Neuenkirch, Andreas
2009-01-01
In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases
Adaptive control of chaotic systems with stochastic time varying unknown parameters
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2008-10-15
In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment.
A two-stage stochastic programming approach for operating multi-energy systems
DEFF Research Database (Denmark)
Zeng, Qing; Fang, Jiakun; Chen, Zhe
2017-01-01
This paper provides a two-stage stochastic programming approach for joint operating multi-energy systems under uncertainty. Simulation is carried out in a test system to demonstrate the feasibility and efficiency of the proposed approach. The test energy system includes a gas subsystem with a gas...
The response analysis of fractional-order stochastic system via generalized cell mapping method.
Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei
2018-01-01
This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.
Global behavior analysis for stochastic system of 1,3-PD continuous fermentation
Zhu, Xi; Kliemann, Wolfgang; Li, Chunfa; Feng, Enmin; Xiu, Zhilong
2017-12-01
Global behavior for stochastic system of continuous fermentation in glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae is analyzed in this paper. This bioprocess cannot avoid the stochastic perturbation caused by internal and external disturbance which reflect on the growth rate. These negative factors can limit and degrade the achievable performance of controlled systems. Based on multiplicity phenomena, the equilibriums and bifurcations of the deterministic system are analyzed. Then, a stochastic model is presented by a bounded Markov diffusion process. In order to analyze the global behavior, we compute the control sets for the associated control system. The probability distributions of relative supports are also computed. The simulation results indicate that how the disturbed biosystem tend to stationary behavior globally.
A higher-order numerical framework for stochastic simulation of chemical reaction systems.
Székely, Tamás
2012-07-15
BACKGROUND: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system. RESULTS: By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint τ-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and θ-trapezoidal τ-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. CONCLUSIONS: Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.
ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process
Directory of Open Access Journals (Sweden)
E. K. Boukas
2004-01-01
Full Text Available This paper considers the stabilization problem of the class of continuous-time linear stochastic hybrid systems with Wiener process. The ℋ∞ state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI-based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.
International Nuclear Information System (INIS)
Li Jinghui
2008-01-01
In this paper, an electric system with two dichotomous resistors is investigated. It is shown that this system can display two stochastic resonances, which are the amplitude of the periodic response as the functions of the two dichotomous resistors strengthes respectively. In the limits of Gaussian white noise and shot white noise (i.e., the two noises are both Gaussian white noise or shot white noise), no phenomena of resonance appear. By further study, we find that when the system is with three or more multiplicative telegraphic noises, there are three or more stochastic resonances
A penalty guided stochastic fractal search approach for system reliability optimization
International Nuclear Information System (INIS)
Mellal, Mohamed Arezki; Zio, Enrico
2016-01-01
Modern industry requires components and systems with high reliability levels. In this paper, we address the system reliability optimization problem. A penalty guided stochastic fractal search approach is developed for solving reliability allocation, redundancy allocation, and reliability–redundancy allocation problems. Numerical results of ten case studies are presented as benchmark problems for highlighting the superiority of the proposed approach compared to others from literature. - Highlights: • System reliability optimization is investigated. • A penalty guided stochastic fractal search approach is developed. • Results of ten case studies are compared with previously published methods. • Performance of the approach is demonstrated.
Stabilizing simulations of complex stochastic representations for quantum dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Perret, C; Petersen, W P, E-mail: wpp@math.ethz.ch [Seminar for Applied Mathematics, ETH, Zurich (Switzerland)
2011-03-04
Path integral representations of quantum dynamics can often be formulated as stochastic differential equations (SDEs). In a series of papers, Corney and Drummond (2004 Phys. Rev. Lett. 93 260401), Deuar and Drummond (2001 Comput. Phys. Commun. 142 442-5), Drummond and Gardnier (1980 J. Phys. A: Math. Gen. 13 2353-68), Gardiner and Zoller (2004 Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Series in Synergetics) 3rd edn (Berlin: Springer)) and Gilchrist et al (1997 Phys. Rev. A 55 3014-32) and their collaborators have derived SDEs from coherent states representations for density matrices. Computationally, these SDEs are attractive because they seem simple to simulate. They can be quite unstable, however. In this paper, we consider some of the instabilities and propose a few remedies. Particularly, because the variances of the simulated paths typically grow exponentially, the processes become de-localized in relatively short times. Hence, the issues of boundary conditions and stable integration methods become important. We use the Bose-Einstein Hamiltonian as an example. Our results reveal that it is possible to significantly extend integration times and show the periodic structure of certain functionals.
H∞ Filtering for Networked Markovian Jump Systems with Multiple Stochastic Communication Delays
Directory of Open Access Journals (Sweden)
Hui Dong
2015-01-01
Full Text Available This paper is concerned with the H∞ filtering for a class of networked Markovian jump systems with multiple communication delays. Due to the existence of communication constraints, the measurement signal cannot arrive at the filter completely on time, and the stochastic communication delays are considered in the filter design. Firstly, a set of stochastic variables is introduced to model the occurrence probabilities of the delays. Then based on the stochastic system approach, a sufficient condition is obtained such that the filtering error system is stable in the mean-square sense and with a prescribed H∞ disturbance attenuation level. The optimal filter gain parameters can be determined by solving a convex optimization problem. Finally, a simulation example is given to show the effectiveness of the proposed filter design method.
Directory of Open Access Journals (Sweden)
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
A constrained approach to multiscale stochastic simulation of chemically reacting systems
Cotter, Simon L.
2011-01-01
Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. © 2011 American Institute of Physics.
STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB.
Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K
2011-04-15
The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user's models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. The software is open source under the GPL v3 and available at http://www.maths.ox.ac.uk/cmb/STOCHSIMGPU. The web site also contains supplementary information. klingbeil@maths.ox.ac.uk Supplementary data are available at Bioinformatics online.
International Nuclear Information System (INIS)
Kang-Kang, Wang; Xian-Bin, Liu; Yu, Zhou
2015-01-01
In this paper, the stability and stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal for a metapopulation system driven by the additive Gaussian noise, multiplicative non-Gaussian noise and noise correlation time is investigated. By using the fast descent method, unified colored noise approximation and McNamara and Wiesenfeld’s SR theory, the analytical expressions of the stationary probability distribution function and signal-to-noise ratio (SNR) are derived in the adiabatic limit. Via numerical calculations, each effect of the addictive noise intensity, the multiplicative noise intensity and the correlation time upon the steady state probability distribution function and the SNR is discussed, respectively. It is shown that multiplicative, additive noises and the departure parameter from the Gaussian noise can all destroy the stability of the population system. However, the noise correlation time can consolidate the stability of the system. On the other hand, the correlation time always plays an important role in motivating the SR and enhancing the SNR. Under different parameter conditions of the system, the multiplicative, additive noises and the departure parameter can not only excite SR phenomenon, but also restrain the SR phenomenon, which demonstrates the complexity of different noises upon the nonlinear system. (paper)
A stochastic process model for life cycle cost analysis of nuclear power plant systems
Van der Weide, J.A.M.; Pandey, M.D.
2013-01-01
The paper presents a general stochastic model to analyze the life cycle cost of an engineering system that is affected by minor but repairable failures interrupting the operation and a major failure that would require the replacement or renewal of the failed system. It is commonly observed that the
Approximation of itô integrals arising in stochastic time-delayed systems
Bagchi, Arunabha
1984-01-01
Likelihood functional for stochastic linear time-delayed systems involve Itô integrals with respect to the observed data. Since the Wiener process appearing in the standard observation process model for such systems is not realizable and the physically observed process is smooth, one needs to study
Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun
2015-12-01
This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.
A Class of Stochastic Hybrid Systems with State-Dependent Switching Noise
DEFF Research Database (Denmark)
Leth, John-Josef; Rasmussen, Jakob Gulddahl; Schiøler, Henrik
2012-01-01
In this paper, we develop theoretical results based on a proposed method for modeling switching noise for a class of hybrid systems with piecewise linear partitioned state space, and state-depending switching. We devise a stochastic model of such systems, whose global dynamics is governed...
Kiesmüller, G.P.
2003-01-01
This paper addresses the control problem of a stochastic recovery system with two stocking points and different leadtimes for production and remanufacturing. For such systems the optimal control policy for a linear cost model is not known. Therefore, in the literature several heuristic policies are
ON THE ANISOTROPIC NORM OF DISCRETE TIME STOCHASTIC SYSTEMS WITH STATE DEPENDENT NOISE
Directory of Open Access Journals (Sweden)
Isaac Yaesh
2013-01-01
Full Text Available The purpose of this paper is to determine conditions for the bound-edness of the anisotropic norm of discrete-time linear stochastic sys-tems with state dependent noise. It is proved that these conditions canbe expressed in terms of the feasibility of a specific system of matrixinequalities.
Stochastic Modeling of Usage Patterns in a Web-Based Information System.
Chen, Hui-Min; Cooper, Michael D.
2002-01-01
Uses continuous-time stochastic models, mainly based on semi-Markov chains, to derive user state transition patterns, both in rates and in probabilities, in a Web-based information system. Describes search sessions from transaction logs of the University of California's MELVYL library catalog system and discusses sequential dependency. (Author/LRW)
Directory of Open Access Journals (Sweden)
Yajun Li
2015-01-01
Full Text Available This paper deals with the robust H∞ filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribed H∞ performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
International Nuclear Information System (INIS)
Liu Di
2008-01-01
We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples
Parallel Stochastic discrete event simulation of calcium dynamics in neuron.
Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W
2017-09-26
The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.
A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.
Directory of Open Access Journals (Sweden)
Lufang Zhou
2010-01-01
Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the
Design and analysis of stochastic DSS query optimizers in a distributed database system
Directory of Open Access Journals (Sweden)
Manik Sharma
2016-07-01
Full Text Available Query optimization is a stimulating task of any database system. A number of heuristics have been applied in recent times, which proposed new algorithms for substantially improving the performance of a query. The hunt for a better solution still continues. The imperishable developments in the field of Decision Support System (DSS databases are presenting data at an exceptional rate. The massive volume of DSS data is consequential only when it is able to access and analyze by distinctive researchers. Here, an innovative stochastic framework of DSS query optimizer is proposed to further optimize the design of existing query optimization genetic approaches. The results of Entropy Based Restricted Stochastic Query Optimizer (ERSQO are compared with the results of Exhaustive Enumeration Query Optimizer (EAQO, Simple Genetic Query Optimizer (SGQO, Novel Genetic Query Optimizer (NGQO and Restricted Stochastic Query Optimizer (RSQO. In terms of Total Costs, EAQO outperforms SGQO, NGQO, RSQO and ERSQO. However, stochastic approaches dominate in terms of runtime. The Total Costs produced by ERSQO is better than SGQO, NGQO and RGQO by 12%, 8% and 5% respectively. Moreover, the effect of replicating data on the Total Costs of DSS query is also examined. In addition, the statistical analysis revealed a 2-tailed significant correlation between the number of join operations and the Total Costs of distributed DSS query. Finally, in regard to the consistency of stochastic query optimizers, the results of SGQO, NGQO, RSQO and ERSQO are 96.2%, 97.2%, 97.45 and 97.8% consistent respectively.
Directory of Open Access Journals (Sweden)
Zengyun Wang
2013-01-01
Full Text Available This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Cotter, Simon L.; Vejchodský , Tomá š; Erban, Radek
2013-01-01
Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.
On one model problem for the reaction-diffusion-advection equation
Davydova, M. A.; Zakharova, S. A.; Levashova, N. T.
2017-09-01
The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.
Nefedov, Nikolay
2017-02-01
This is an extended variant of the paper presented at MURPHYS-HSFS 2016 conference in Barcelona. We discuss further development of the asymptotic method of differential inequalities to investigate existence and stability of sharp internal layers (fronts) for nonlinear singularly perturbed periodic parabolic problems and initial boundary value problems with blow-up of fronts for reaction-diffusion-advection equations. In particular, we consider periodic solutions with internal layer in the case of balanced reaction. For the initial boundary value problems we prove the existence of fronts and give their asymptotic approximation including the new case of blowing-up fronts. This case we illustrate by the generalised Burgers equation.
Directory of Open Access Journals (Sweden)
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Energy Technology Data Exchange (ETDEWEB)
Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms
International Nuclear Information System (INIS)
Sheng Li; Yang Huizhong; Lou Xuyang
2009-01-01
This paper presents an exponential synchronization scheme for a class of neural networks with time-varying and distributed delays and reaction-diffusion terms. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory. At the same time, the update laws of parameters are proposed to guarantee the synchronization of delayed neural networks with all parameters unknown. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.
Identification of a Discontinuous Parameter in Stochastic Parabolic Systems
International Nuclear Information System (INIS)
Aihara, S. I.
1998-01-01
The purpose of this paper is to study the identification problem for a spatially varying discontinuous parameter in stochastic diffusion equations. The consistency property of the maximum likelihood estimate (M.L.E.) and a generating algorithm for M.L.E. have been explored under the condition that the unknown parameter is in a sufficiently regular space with respect to spatial variables. In order to prove the consistency property of the M.L.E. for a discontinuous diffusion coefficient, we use the method of sieves, i.e., first the admissible class of unknown parameters is projected into a finite-dimensional space and next the convergence of the derived finite-dimensional M.L.E. to the infinite-dimensional M.L.E. is justified under some conditions. An iterative algorithm for generating the M.L.E. is also proposed with two numerical examples
Stochastic control applied to the ISWEC Wave Energy System
International Nuclear Information System (INIS)
Bracco, Giovanni; Casassa, Maria; Giorcelli, Ermanno; Mattiazzo, Giuliana; Passione, Biagio; Raffero, Mattia; Vissio, Giacomo; Martini, Michele
2015-01-01
ISWEC (Inertial Sea Wave Energy Converter) is a floating marine device able to harvest sea waves energy by the interaction between the pitching motion of a floater and a spinning flywheel which can drive an electric PTO. In the ISWEC the hull dynamics is governed and controlled by the gyroscopic torque. The optimal control logic results in tuning the floater dynamics to the incoming waves in order to maximize the power transfer from the waves to the floater. In this paper the control problems of the ISWEC are stated and a control scheme based on the sub-optimal stochastic control logic is presented. The control scheme here presented has been tested using real wave records acquired at the deployment location in Pantelleria Island, which is one of the most energetic sites of the Mediterranean Sea.
Wang, Sheng; Wang, Linshan; Wei, Tengda
2018-04-01
This paper concerns the dynamics of a stochastic predator-prey system with Markovian switching and Lévy noise. First, the existence and uniqueness of global positive solution to the system is proved. Then, by combining stochastic analytical techniques with M-matrix analysis, sufficient conditions of stochastic permanence and extinction are obtained. Furthermore, for the stochastic permanence case, by means of four constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated. Finally, our conclusions are illustrated through an example.
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
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Jie Ran
2015-01-01
Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.
Energy Technology Data Exchange (ETDEWEB)
Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)
2014-07-04
To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.
A fuzzy-stochastic power system planning model: Reflection of dual objectives and dual uncertainties
International Nuclear Information System (INIS)
Zhang, X.Y.; Huang, G.H.; Zhu, H.; Li, Y.P.
2017-01-01
In this study, a fuzzy stochastic dynamic fractional programming (FSDFP) method is proposed for supporting sustainable management of electric power system (EPS) under dual uncertainties. As an improvement upon the mixed-integer linear fractional programming, FSDFP can not only tackle multi-objective issues effectively without setting weights, but also can deal with uncertain parameters which have both stochastic and fuzzy characteristics. Thus, the developed method can help provide valuable information for supporting capacity-expansion planning and in-depth policy analysis of EPS management problems. For demonstrating these advantages, FSDFP has been applied to a case study of a typical regional EPS planning, where the decision makers have to deal with conflicts between economic development that maximizes the system profit and environmental protection that minimizes the carbon dioxide emissions. The obtained results can be analyzed to generate several decision alternatives, and can then help decision makers make suitable decisions under different input scenarios. Furthermore, comparisons of the solution from FSDFP method with that from fuzzy stochastic dynamic linear programming, linear fractional programming and dynamic stochastic fractional programming methods are undertaken. The contrastive analysis reveals that FSDFP is a more effective approach that can better characterize the complexities and uncertainties of real EPS management problems. - Highlights: • A fuzzy stochastic dynamic fractional programming (FSDFP) method is proposed. • FSDFP can address multiple conflicting objectives without setting weights. • FSDFP can reflect dual uncertainties with both stochastic and fuzzy characteristics. • Some reasonable solutions for a case of power system sustainable planning are generated. • Comparisons of the solutions from FSDFP with other optimization methods are undertaken.
Optimal control strategy for an impulsive stochastic competition system with time delays and jumps
Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua
2017-07-01
Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.
Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience
Directory of Open Access Journals (Sweden)
Yan Chen
2017-01-01
Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.
Liu, Xiangdong; Li, Qingze; Pan, Jianxin
2018-06-01
Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.
Effects of error feedback on a nonlinear bistable system with stochastic resonance
International Nuclear Information System (INIS)
Li Jian-Long; Zhou Hui
2012-01-01
In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing
Darmon, David
2018-03-01
In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.
Path integral methods for the dynamics of stochastic and disordered systems
DEFF Research Database (Denmark)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...
International Nuclear Information System (INIS)
Frank, T.D.
2006-01-01
First-order approximations of time-dependent solutions are determined for stochastic systems perturbed by time-delayed feedback forces. To this end, the theory of delay Fokker-Planck equations is applied in combination with Bayes' theorem. Applications to a time-delayed Ornstein-Uhlenbeck process and the geometric Brownian walk of financial physics are discussed
Directory of Open Access Journals (Sweden)
C. Parthasarathy
2013-03-01
Full Text Available In this paper, we study the controllability results of first order impulsive stochastic differential and neutral differential systems with state-dependent delay by using semigroup theory. The controllability results are derived by the means of Leray-SchauderAlternative fixed point theorem. An example is provided to illustrate the theory.
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Dammann, Bernd; Madsen, Henrik
2014-01-01
This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP...
Stochastic long term modelling of a drainage system with estimation of return period uncertainty
DEFF Research Database (Denmark)
Thorndahl, Søren
2009-01-01
Long term prediction of maximum water levels and combined sewer overflow (CSO) in drainage systems are associated with large uncertainties. Especially on rainfall inputs, parameters, and assessment of return periods. This paper proposes a Monte Carlo based methodology for stochastic prediction of...
Arjunan, Satya Nanda Vel; Tomita, Masaru
2010-03-01
Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally. The online version of this article (doi:10.1007/s11693-009-9047-2) contains supplementary material, which is available to
Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida
2014-05-01
Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.
Haji Ali, Abdul Lateef
2016-01-01
I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
Haji Ali, Abdul Lateef
2016-01-08
I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
A Newton-Based Extremum Seeking MPPT Method for Photovoltaic Systems with Stochastic Perturbations
Directory of Open Access Journals (Sweden)
Heng Li
2014-01-01
Full Text Available Microcontroller based maximum power point tracking (MPPT has been the most popular MPPT approach in photovoltaic systems due to its high flexibility and efficiency in different photovoltaic systems. It is well known that PV systems typically operate under a range of uncertain environmental parameters and disturbances, which implies that MPPT controllers generally suffer from some unknown stochastic perturbations. To address this issue, a novel Newton-based stochastic extremum seeking MPPT method is proposed. Treating stochastic perturbations as excitation signals, the proposed MPPT controller has a good tolerance of stochastic perturbations in nature. Different from conventional gradient-based extremum seeking MPPT algorithm, the convergence rate of the proposed controller can be totally user-assignable rather than determined by unknown power map. The stability and convergence of the proposed controller are rigorously proved. We further discuss the effects of partial shading and PV module ageing on the proposed controller. Numerical simulations and experiments are conducted to show the effectiveness of the proposed MPPT algorithm.
A Stochastic Hybrid Systems framework for analysis of Markov reward models
International Nuclear Information System (INIS)
Dhople, S.V.; DeVille, L.; Domínguez-García, A.D.
2014-01-01
In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: (i) a discrete state that describes the possible configurations/modes that a system can adopt, which includes the nominal (non-faulty) operational mode, but also those operational modes that arise due to component faults, and (ii) a continuous state that describes the reward. Discrete state transitions are stochastic, and governed by transition rates that are (in general) a function of time and the value of the continuous state. The evolution of the continuous state is described by a stochastic differential equation and reward measures are defined as functions of the continuous state. Additionally, each transition is associated with a reset map that defines the mapping between the pre- and post-transition values of the discrete and continuous states; these mappings enable the definition of impulses and losses in the reward. The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models. We illustrate the application of the framework to performability analysis via analytical and numerical examples
International Nuclear Information System (INIS)
Qian, Hong
2014-01-01
We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase space while in equilibrium with a heat bath. The theory generalizes underdamped mechanical equilibrium: dx=gdt+{−D∇ϕdt+√(2D)dB(t)}, with ∇⋅g=0 and {⋯} respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution u ss (x)=e −ϕ(x) . We find an orthogonality ∇ϕ⋅g=0 as a hallmark of the system. Stochastic thermodynamics based on time reversal (t,ϕ,g)→(−t,ϕ,−g) is formulated: entropy production e p # (t)=−dF(t)/dt; generalized “heat” h d # (t)=−dU(t)/dt, U(t)=∫ R n ϕ(x)u(x,t)dx being “internal energy”, and “free energy” F(t)=U(t)+∫ R n u(x,t)lnu(x,t)dx never increases. Entropy follows (dS)/(dt) =e p # −h d # . Our formulation is shown to be consistent with an earlier theory of P. Ao. Its contradistinctions to other theories, potential-flux decomposition, stochastic Hamiltonian system with even and odd variables, Klein–Kramers equation, Freidlin–Wentzell's theory, and GENERIC, are discussed.
Weisheimer, Antje; Corti, Susanna; Palmer, Tim; Vitart, Frederic
2014-01-01
The finite resolution of general circulation models of the coupled atmosphere–ocean system and the effects of sub-grid-scale variability present a major source of uncertainty in model simulations on all time scales. The European Centre for Medium-Range Weather Forecasts has been at the forefront of developing new approaches to account for these uncertainties. In particular, the stochastically perturbed physical tendency scheme and the stochastically perturbed backscatter algorithm for the atmosphere are now used routinely for global numerical weather prediction. The European Centre also performs long-range predictions of the coupled atmosphere–ocean climate system in operational forecast mode, and the latest seasonal forecasting system—System 4—has the stochastically perturbed tendency and backscatter schemes implemented in a similar way to that for the medium-range weather forecasts. Here, we present results of the impact of these schemes in System 4 by contrasting the operational performance on seasonal time scales during the retrospective forecast period 1981–2010 with comparable simulations that do not account for the representation of model uncertainty. We find that the stochastic tendency perturbation schemes helped to reduce excessively strong convective activity especially over the Maritime Continent and the tropical Western Pacific, leading to reduced biases of the outgoing longwave radiation (OLR), cloud cover, precipitation and near-surface winds. Positive impact was also found for the statistics of the Madden–Julian oscillation (MJO), showing an increase in the frequencies and amplitudes of MJO events. Further, the errors of El Niño southern oscillation forecasts become smaller, whereas increases in ensemble spread lead to a better calibrated system if the stochastic tendency is activated. The backscatter scheme has overall neutral impact. Finally, evidence for noise-activated regime transitions has been found in a cluster analysis of mid
A Stochastic Model for Improving Information Security in Supply Chain Systems
Ibrahim Al Kattan; Ahmed Al Nunu; Kassem Saleh
2009-01-01
This article presents a probabilistic security model for supply chain management systems (SCM) in which the basic goals of security (including confidentiality, integrity, availability and accountability, CIAA) are modeled and analyzed. Consequently, the weak points in system security are identified. A stochastic model using measurable values to describe the information system security of a SCM is introduced. Information security is a crucial and integral part of the network of supply chains. ...
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
International Nuclear Information System (INIS)
Gershgorin, B.; Harlim, J.; Majda, A.J.
2010-01-01
The filtering and predictive skill for turbulent signals is often limited by the lack of information about the true dynamics of the system and by our inability to resolve the assumed dynamics with sufficiently high resolution using the current computing power. The standard approach is to use a simple yet rich family of constant parameters to account for model errors through parameterization. This approach can have significant skill by fitting the parameters to some statistical feature of the true signal; however in the context of real-time prediction, such a strategy performs poorly when intermittent transitions to instability occur. Alternatively, we need a set of dynamic parameters. One strategy for estimating parameters on the fly is a stochastic parameter estimation through partial observations of the true signal. In this paper, we extend our newly developed stochastic parameter estimation strategy, the Stochastic Parameterization Extended Kalman Filter (SPEKF), to filtering sparsely observed spatially extended turbulent systems which exhibit abrupt stability transition from time to time despite a stable average behavior. For our primary numerical example, we consider a turbulent system of externally forced barotropic Rossby waves with instability introduced through intermittent negative damping. We find high filtering skill of SPEKF applied to this toy model even in the case of very sparse observations (with only 15 out of the 105 grid points observed) and with unspecified external forcing and damping. Additive and multiplicative bias corrections are used to learn the unknown features of the true dynamics from observations. We also present a comprehensive study of predictive skill in the one-mode context including the robustness toward variation of stochastic parameters, imperfect initial conditions and finite ensemble effect. Furthermore, the proposed stochastic parameter estimation scheme applied to the same spatially extended Rossby wave system demonstrates
International Nuclear Information System (INIS)
Lu Junguo
2008-01-01
In this paper, the global exponential stability and periodicity for a class of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are addressed by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential converge to 0 of the difference between any two solutions of the original reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Furthermore, we prove periodicity of the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Sufficient conditions ensuring the global exponential stability and the existence of periodic oscillatory solutions for the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are given. These conditions are easy to check and have important leading significance in the design and application of reaction-diffusion recurrent neural networks with delays. Finally, two numerical examples are given to show the effectiveness of the obtained results
Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andres [Iowa State Univ., Ames, IA (United States)
2017-08-05
Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use
Directory of Open Access Journals (Sweden)
Pengfei Guo
2014-01-01
Full Text Available This paper deals with the fault detection problem for a class of discrete-time wireless networked control systems described by switching topology with uncertainties and disturbances. System states of each individual node are affected not only by its own measurements, but also by other nodes’ measurements according to a certain network topology. As the topology of system can be switched in a stochastic way, we aim to design H∞ fault detection observers for nodes in the dynamic time-delay systems. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are acquired to guarantee the existence of the filters satisfying the H∞ performance constraint, and observer gains are derived by solving linear matrix inequalities. Finally, an illustrated example is provided to verify the effectiveness of the theoretical results.
Model reduction for slow–fast stochastic systems with metastable behaviour
International Nuclear Information System (INIS)
Bruna, Maria; Chapman, S. Jonathan; Smith, Matthew J.
2014-01-01
The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediated chemical switch coupled to a slower varying species), and one from ecology (a predator–prey system). Numerical simulations of each model reduction are compared with those of the full system
International Nuclear Information System (INIS)
Olsson, Magnus; Perninge, Magnus; Soeder, Lennart
2010-01-01
The inclusion of wind power into power systems has a significant impact on the demand for real-time balancing power due to the stochastic nature of wind power production. The overall aim of this paper is to present probabilistic models of the impact of large-scale integration of wind power on the continuous demand in MW for real-time balancing power. This is important not only for system operators, but also for producers and consumers since they in most systems through various market solutions provide balancing power. Since there can occur situations where the wind power variations cancel out other types of deviations in the system, models on an hourly basis are not sufficient. Therefore the developed model is in continuous time and is based on stochastic differential equations (SDE). The model can be used within an analytical framework or in Monte Carlo simulations. (author)
Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks
Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.
2018-04-01
Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.
Yuvan, Steven; Bier, Martin
2018-02-01
Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.
Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz
2016-06-01
Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
Schwarz, Karsten; Rieger, Heiko
2013-03-01
We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.
A Reaction-Diffusion-Based Coding Rate Control Mechanism for Camera Sensor Networks
Directory of Open Access Journals (Sweden)
Naoki Wakamiya
2010-08-01
Full Text Available A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.
A reaction-diffusion-based coding rate control mechanism for camera sensor networks.
Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki
2010-01-01
A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.
Monostable traveling waves for a time-periodic and delayed nonlocal reaction-diffusion equation
Li, Panxiao; Wu, Shi-Liang
2018-04-01
This paper is concerned with a time-periodic and delayed nonlocal reaction-diffusion population model with monostable nonlinearity. Under quasi-monotone or non-quasi-monotone assumptions, it is known that there exists a critical wave speed c_*>0 such that a periodic traveling wave exists if and only if the wave speed is above c_*. In this paper, we first prove the uniqueness of non-critical periodic traveling waves regardless of whether the model is quasi-monotone or not. Further, in the quasi-monotone case, we establish the exponential stability of non-critical periodic traveling fronts. Finally, we illustrate the main results by discussing two types of death and birth functions arising from population biology.
A decision dependent stochastic process model for repairable systems with applications
Directory of Open Access Journals (Sweden)
Paul F. Zantek
2015-12-01
This paper mathematically formalizes the notion of how management actions impact the functioning of a repairable system over time by developing a new stochastic process model for such systems. The proposed model is illustrated using both simulated and real data. The proposed model compares favorably to other models for well-known data on Boeing airplanes. The model is further illustrated and compared to other models on failure time and maintenance data stemming from the South Texas Project nuclear power plant.
PARAMETRIC IDENTIFICATION OF STOCHASTIC SYSTEM BY NON-GRADIENT RANDOM SEARCHING
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A. A. Lobaty
2017-01-01
Full Text Available At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology. The identification problem is dependent on a priori information about identification object, besides that the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.. The paper considers a problem for determination of system parameters (identification object which is assigned by the stochastic mathematical model including random functions of time. It has been shown that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of parameters in a mathematical model of the stochastic system by non-gradient random searching. A specific feature of the algorithm is its applicability practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm ensures searching of an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.
Yin, Fancheng; Yu, Xiaoyan
2015-01-01
This paper is concerned with the existence of stationary distribution and extinction for multispecies stochastic Lotka-Volterra predator-prey system. The contributions of this paper are as follows. (a) By using Lyapunov methods, the sufficient conditions on existence of stationary distribution and extinction are established. (b) By using the space decomposition technique and the continuity of probability, weaker conditions on extinction of the system are obtained. Finally, a numer...
Moreno, Pablo; García, Marcelo
2016-01-01
The increase in energy consumption, especially in residential consumers, means that the electrical system should grow at pair, in infrastructure and installed capacity, the energy prices vary to meet these needs, so this paper uses the methodology of demand response using stochastic methods such as Markov, to optimize energy consumption of residential users. It is necessary to involve customers in the electrical system because in this way it can be verified the actual amount of electric charg...
SWINE BREEDING SYSTEMS: A STOCHASTIC EVALUATION WITH IMPLICATIONS FOR EMERGING TECHNOLOGY
Massey, Raymond E.; Williams, Joseph E.
1991-01-01
The after-tax net present value for 27 swine breeding systems composed of Duroc, Hampshire, and Yorkshire breeds were simulated and ordered using stochastic dominance analysis. The concept of the value of information was expanded to develop the concept of the willingness to pay to adopt a new technology. For producers not currently using the dominant system, estimates of the allowable present value cost of adoption are reported and used to explain diverse production practices.
Accurate numerical simulation of reaction-diffusion processes for heavy oil recovery
Energy Technology Data Exchange (ETDEWEB)
Govind, P.A.; Srinivasan, S. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)
2008-10-15
This study evaluated a reaction-diffusion simulation tool designed to analyze the displacement of carbon dioxide (CO{sub 2}) in a simultaneous injection of carbon dioxide and elemental sodium in a heavy oil reservoir. Sodium was used due to the exothermic reaction of sodium with in situ that occurs when heat is used to reduce oil viscosity. The process also results in the formation of sodium hydroxide that reduces interfacial tension at the bitumen interface. A commercial simulation tool was used to model the sodium transport mechanism to the reaction interface through diffusion as well as the reaction zone's subsequent displacement. The aim of the study was to verify if the in situ reaction was able to generate sufficient heat to reduce oil viscosity and improve the displacement of the heavy oil. The study also assessed the accuracy of the reaction front simulation tool, in which an alternate method was used to model the propagation front as a moving heat source. The sensitivity of the simulation results were then evaluated in relation to the diffusion coefficient in order to understand the scaling characteristics of the reaction-diffusion zone. A pore-scale simulation was then up-scaled to grid blocks. Results of the study showed that when sodium suspended in liquid CO{sub 2} is injected into reservoirs, it diffuses through the carrier phase and interacts with water. A random walk diffusion algorithm with reactive dissipation was implemented to more accurately characterize reaction and diffusion processes. It was concluded that the algorithm modelled physical dispersion while neglecting the effect of numerical dispersion. 10 refs., 3 tabs., 24 figs.
International Nuclear Information System (INIS)
Brett, Tobias; Galla, Tobias
2014-01-01
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period
Brett, Tobias; Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Stability Criterion of Linear Stochastic Systems Subject to Mixed H2/Passivity Performance
Directory of Open Access Journals (Sweden)
Cheung-Chieh Ku
2015-01-01
Full Text Available The H2 control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, the H2 control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.
Directory of Open Access Journals (Sweden)
Shahid Hasnain
2017-07-01
Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Structure Learning in Stochastic Non-linear Dynamical Systems
Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.
2005-12-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.
A stochastic model for an urea decomposition system
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VSS Yadavalli
2005-12-01
Full Text Available Availability is an important measure in describing the performance of a system. The availability of a decomposition process in an urea production system in the fertilizer industry is considered in this paper. The system contains four subsystems and is supported by a standby unit. An estimation study of the steady state availability of the system is performed and illustrated by means of a numerical example.
Identifying bottlenecks in manufacturing systems using stochastic criticality analysis
Nogueira Bastos, J.P.; van der Sanden, L.J.; Donk, O.; Voeten, J.P.M.; Stuijk, S.; Schiffelers, R.R.H.; Corporaal, H.
2018-01-01
System design is a difficult process with many design-choices for which the impact may be difficult to foresee. Manufacturing system design is no exception to this. Increased use of flexible manufacturing systems which are able to perform different operations/use-cases further raises the design
Wang, Jianhui; Liu, Zhi; Chen, C L Philip; Zhang, Yun
2017-10-12
Hysteresis exists ubiquitously in physical actuators. Besides, actuator failures/faults may also occur in practice. Both effects would deteriorate the transient tracking performance, and even trigger instability. In this paper, we consider the problem of compensating for actuator failures and input hysteresis by proposing a fuzzy control scheme for stochastic nonlinear systems. Compared with the existing research on stochastic nonlinear uncertain systems, it is found that how to guarantee a prescribed transient tracking performance when taking into account actuator failures and hysteresis simultaneously also remains to be answered. Our proposed control scheme is designed on the basis of the fuzzy logic system and backstepping techniques for this purpose. It is proven that all the signals remain bounded and the tracking error is ensured to be within a preestablished bound with the failures of hysteretic actuator. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.
Sliding mode control-based linear functional observers for discrete-time stochastic systems
Singh, Satnesh; Janardhanan, Sivaramakrishnan
2017-11-01
Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.
Modeling reliability of power systems substations by using stochastic automata networks
International Nuclear Information System (INIS)
Šnipas, Mindaugas; Radziukynas, Virginijus; Valakevičius, Eimutis
2017-01-01
In this paper, stochastic automata networks (SANs) formalism to model reliability of power systems substations is applied. The proposed strategy allows reducing the size of state space of Markov chain model and simplifying system specification. Two case studies of standard configurations of substations are considered in detail. SAN models with different assumptions were created. SAN approach is compared with exact reliability calculation by using a minimal path set method. Modeling results showed that total independence of automata can be assumed for relatively small power systems substations with reliable equipment. In this case, the implementation of Markov chain model by a using SAN method is a relatively easy task. - Highlights: • We present the methodology to apply stochastic automata network formalism to create Markov chain models of power systems. • The stochastic automata network approach is combined with minimal path sets and structural functions. • Two models of substation configurations with different model assumptions are presented to illustrate the proposed methodology. • Modeling results of system with independent automata and functional transition rates are similar. • The conditions when total independence of automata can be assumed are addressed.
International Nuclear Information System (INIS)
Wang Xiaohu; Xu Daoyi
2009-01-01
In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.
Analytic descriptions of stochastic bistable systems under force ramp.
Friddle, Raymond W
2016-05-01
Solving the two-state master equation with time-dependent rates, the ubiquitous driven bistable system, is a long-standing problem that does not permit a complete solution for all driving rates. Here we show an accurate approximation to this problem by considering the system in the control parameter regime. The results are immediately applicable to a diverse range of bistable systems including single-molecule mechanics.
International Nuclear Information System (INIS)
Hsiang, J.-T.; Hu, B.L.
2015-01-01
The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics. -- Highlights: •Nonequilibrium steady state (NESS) for interacting quantum many-body systems. •Derivation of stochastic equations for quantum oscillator chain with two heat baths. •Explicit calculation of the energy flow from one bath to the
Stochastic Methods Applied to Power System Operations with Renewable Energy: A Review
Energy Technology Data Exchange (ETDEWEB)
Zhou, Z. [Argonne National Lab. (ANL), Argonne, IL (United States); Liu, C. [Argonne National Lab. (ANL), Argonne, IL (United States); Electric Reliability Council of Texas (ERCOT), Austin, TX (United States); Botterud, A. [Argonne National Lab. (ANL), Argonne, IL (United States)
2016-08-01
Renewable energy resources have been rapidly integrated into power systems in many parts of the world, contributing to a cleaner and more sustainable supply of electricity. Wind and solar resources also introduce new challenges for system operations and planning in terms of economics and reliability because of their variability and uncertainty. Operational strategies based on stochastic optimization have been developed recently to address these challenges. In general terms, these stochastic strategies either embed uncertainties into the scheduling formulations (e.g., the unit commitment [UC] problem) in probabilistic forms or develop more appropriate operating reserve strategies to take advantage of advanced forecasting techniques. Other approaches to address uncertainty are also proposed, where operational feasibility is ensured within an uncertainty set of forecasting intervals. In this report, a comprehensive review is conducted to present the state of the art through Spring 2015 in the area of stochastic methods applied to power system operations with high penetration of renewable energy. Chapters 1 and 2 give a brief introduction and overview of power system and electricity market operations, as well as the impact of renewable energy and how this impact is typically considered in modeling tools. Chapter 3 reviews relevant literature on operating reserves and specifically probabilistic methods to estimate the need for system reserve requirements. Chapter 4 looks at stochastic programming formulations of the UC and economic dispatch (ED) problems, highlighting benefits reported in the literature as well as recent industry developments. Chapter 5 briefly introduces alternative formulations of UC under uncertainty, such as robust, chance-constrained, and interval programming. Finally, in Chapter 6, we conclude with the main observations from our review and important directions for future work.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yishen [Univ. of Washington, Seattle, WA (United States); Argonne National Lab. (ANL), Argonne, IL (United States); Zhou, Zhi [Argonne National Lab. (ANL), Argonne, IL (United States); Liu, Cong [Argonne National Lab. (ANL), Argonne, IL (United States); Electric Reliability Council of Texas (ERCOT), Austin, TX (United States); Botterud, Audun [Argonne National Lab. (ANL), Argonne, IL (United States)
2016-08-01
As more wind power and other renewable resources are being integrated into the electric power grid, the forecast uncertainty brings operational challenges for the power system operators. In this report, different operational strategies for uncertainty management are presented and evaluated. A comprehensive and consistent simulation framework is developed to analyze the performance of different reserve policies and scheduling techniques under uncertainty in wind power. Numerical simulations are conducted on a modified version of the IEEE 118-bus system with a 20% wind penetration level, comparing deterministic, interval, and stochastic unit commitment strategies. The results show that stochastic unit commitment provides a reliable schedule without large increases in operational costs. Moreover, decomposition techniques, such as load shift factor and Benders decomposition, can help in overcoming the computational obstacles to stochastic unit commitment and enable the use of a larger scenario set to represent forecast uncertainty. In contrast, deterministic and interval unit commitment tend to give higher system costs as more reserves are being scheduled to address forecast uncertainty. However, these approaches require a much lower computational effort Choosing a proper lower bound for the forecast uncertainty is important for balancing reliability and system operational cost in deterministic and interval unit commitment. Finally, we find that the introduction of zonal reserve requirements improves reliability, but at the expense of higher operational costs.
Can we observe open loop transfer functions in a stochastic feedback system ?
International Nuclear Information System (INIS)
Kishida, Kuniharu; Suda, Nobuhide.
1991-01-01
There are two kinds of problems concerning open loop and closed loop transfer functions in a feedback system. One is a problem even in the deterministic case, and the other is in the stochastic case. In the deterministic case it is guaranteed under a necessary and sufficient condition that total sum of degrees of sub-transfer functions coincides to the degree of the total system. In the stochastic case a systematic understanding of a physical state model, a theoretical innovation model and a data-oriented innovation model is indispensable for determination of open loop transfer functions from time series data. Undesirable factors appear in determination of open loop transfer functions, since a transfer function matrix from input noises to output variables has a redundancy factor of diagonal matrix. (author)
Risk-sensitive control of stochastic hybrid systems on infinite time horizon
Directory of Open Access Journals (Sweden)
Runolfsson Thordur
1999-01-01
Full Text Available A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive and H ∞ control in the nonhybrid case does not hold for stochastic hybrid systems.
International Nuclear Information System (INIS)
Gomes, I.L.R.; Pousinho, H.M.I.; Melício, R.; Mendes, V.M.F.
2017-01-01
This paper presents an optimal bid submission in a day-ahead electricity market for the problem of joint operation of wind with photovoltaic power systems having an energy storage device. Uncertainty not only due to the electricity market price, but also due to wind and photovoltaic powers is one of the main characteristics of this submission. The problem is formulated as a two-stage stochastic programming problem. The optimal bids and the energy flow in the batteries are the first-stage variables and the energy deviation is the second stage variable of the problem. Energy storage is a way to harness renewable energy conversion, allowing the store and discharge of energy at conveniently market prices. A case study with data from the Iberian day-ahead electricity market is presented and a comparison between joint and disjoint operations is discussed. - • Joint wind and PV systems with energy storage. • Electricity markets. • Stochastic optimization. • Day-ahead market.
Multistage Stochastic Programming and its Applications in Energy Systems Modeling and Optimization
Golari, Mehdi
Electric energy constitutes one of the most crucial elements to almost every aspect of life of people. The modern electric power systems face several challenges such as efficiency, economics, sustainability, and reliability. Increase in electrical energy demand, distributed generations, integration of uncertain renewable energy resources, and demand side management are among the main underlying reasons of such growing complexity. Additionally, the elements of power systems are often vulnerable to failures because of many reasons, such as system limits, weak conditions, unexpected events, hidden failures, human errors, terrorist attacks, and natural disasters. One common factor complicating the operation of electrical power systems is the underlying uncertainties from the demands, supplies and failures of system components. Stochastic programming provides a mathematical framework for decision making under uncertainty. It enables a decision maker to incorporate some knowledge of the intrinsic uncertainty into the decision making process. In this dissertation, we focus on application of two-stage and multistage stochastic programming approaches to electric energy systems modeling and optimization. Particularly, we develop models and algorithms addressing the sustainability and reliability issues in power systems. First, we consider how to improve the reliability of power systems under severe failures or contingencies prone to cascading blackouts by so called islanding operations. We present a two-stage stochastic mixed-integer model to find optimal islanding operations as a powerful preventive action against cascading failures in case of extreme contingencies. Further, we study the properties of this problem and propose efficient solution methods to solve this problem for large-scale power systems. We present the numerical results showing the effectiveness of the model and investigate the performance of the solution methods. Next, we address the sustainability issue
Relationships of dispersive mass transport and stochastic convective flow through hydrologic systems
International Nuclear Information System (INIS)
Simmons, C.S.
1981-01-01
Uncertainty in water flow velocity appears to be a major factor in determining the magnitude of contaminant dispersion expected in a ground water system. This report discusses some concepts and mathematical methods relating dispersive contaminant transport to stochastic aspects of ground water flow. The theory developed should not be construed as absolutely rigorous mathematics, but is presented with the intention of clarifying the physical concepts
Energy Technology Data Exchange (ETDEWEB)
Liu, Yunlong; Wang, Aiping; Guo, Lei; Wang, Hong
2017-07-09
This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.
Joint market clearing in a stochastic framework considering power system security
International Nuclear Information System (INIS)
Aghaei, J.; Shayanfar, H.A.; Amjady, N.
2009-01-01
This paper presents a new stochastic framework for provision of reserve requirements (spinning and non-spinning reserves) as well as energy in day-ahead simultaneous auctions by pool-based aggregated market scheme. The uncertainty of generating units in the form of system contingencies are considered in the market clearing procedure by the stochastic model. The solution methodology consists of two stages, which firstly, employs Monte-Carlo Simulation (MCS) for random scenario generation. Then, the stochastic market clearing procedure is implemented as a series of deterministic optimization problems (scenarios) including non-contingent scenario and different post-contingency states. The objective function of each of these deterministic optimization problems consists of offered cost function (including both energy and reserves offer costs), Lost Opportunity Cost (LOC) and Expected Interruption Cost (EIC). Each optimization problem is solved considering AC power flow and security constraints of the power system. The model is applied to the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS) and simulation studies are carried out to examine the effectiveness of the proposed method.
Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale
Energy Technology Data Exchange (ETDEWEB)
Zabaras, Nicolas J. [Cornell Univ., Ithaca, NY (United States)
2016-11-08
Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.
Improving the performance of power-limited transverse stochastic cooling systems
International Nuclear Information System (INIS)
Goldberg, D.A.; Lambertson, G.R.
1989-08-01
We present the formulas relevant to the behavior of (transverse) stochastic cooling systems which operate under the not uncommon condition that performance is limited by available output power, and contrast the operation of such systems with non-power-limited ones. In particular, we show that for power-limited systems, the two most effective improvements are the use of pickups/kickers which operate in both planes simultaneously and/or plunging of the cooling system electrodes, and present an example where increasing bandwidth is counter-productive. We apply our results to the proposed upgrade of the Fermilab bar p source. 4 refs., 1 fig., 2 tabs
Integral-based event triggering controller design for stochastic LTI systems via convex optimisation
Mousavi, S. H.; Marquez, H. J.
2016-07-01
The presence of measurement noise in the event-based systems can lower system efficiency both in terms of data exchange rate and performance. In this paper, an integral-based event triggering control system is proposed for LTI systems with stochastic measurement noise. We show that the new mechanism is robust against noise and effectively reduces the flow of communication between plant and controller, and also improves output performance. Using a Lyapunov approach, stability in the mean square sense is proved. A simulated example illustrates the properties of our approach.
Steady State Analysis of Stochastic Systems with Multiple Time Delays
Xu, W.; Sun, C. Y.; Zhang, H. Q.
In this paper, attention is focused on the steady state analysis of a class of nonlinear dynamic systems with multi-delayed feedbacks driven by multiplicative correlated Gaussian white noises. The Fokker-Planck equations for delayed variables are at first derived by Novikov's theorem. Then, under small delay assumption, the approximate stationary solutions are obtained by the probability density approach. As a special case, the effects of multidelay feedbacks and the correlated additive and multiplicative Gaussian white noises on the response of a bistable system are considered. It is shown that the obtained analytical results are in good agreement with experimental results in Monte Carlo simulations.
Measurability and Safety Verification for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
Fränzle, Martin; Hahn, Ernst Moritz; Hermanns, Holger
2011-01-01
method that establishes safe upper bounds on reachability probabilities. To arrive there requires us to solve semantic intricacies as well as practical problems. In particular, we show that measurability of a complete system follows from the measurability of its constituent parts. On the practical side......-time behaviour is given by differential equations, as for usual hybrid systems, but the targets of discrete jumps are chosen by probability distributions. These distributions may be general measures on state sets. Also non-determinism is supported, and the latter is exploited in an abstraction and evaluation...
Analysis of dynamic characteristics of stochastic influences in cognitive systems
Directory of Open Access Journals (Sweden)
Alexander A. Solodov
2017-01-01
Full Text Available The aim of the study is to provide an analytical description of the dynamics of the processes to form images in the cognitive system and their subsequent processing by the consciousness, as well as the study of the simplest characteristics of the quality of the cognitive system functioning in the form of the signal/noise ratio.In accordance with the ideas of the cognitive theory, it is believed that images (schemes, categories, Gestalt, systems, archetypes, etc. are firstly generated in the human brain and then processed by the consciousness.These images are formed at random in time and are characterized by a random force of effects and subsequently processed by the consciousness.The images are characterized by random numbers, the common interpretation of which is the amount of information corresponding to the appearance of a certain image. The times of appearance are points on the time axis; their number and position are random as well.The work consists of a logically completed model including the following components:• Justification of a statistical model of the appearance of effects during the operation of the cognitive system in the form of the Poisson point process, characterized by the intensity of occurrence of effects and the random values of those effects.• Development of a mathematical model in the consciousness processing of the random effects in the form of reducing response function, which depends on the current time, the time of occurrence of effects and the magnitudes of these effects. To obtain applied results, exponential response function was applied and the analytical results for the mathematical expectations of the processed and not processed information by the consciousness were received.• Introduction for consideration of the signal/noise ratio, characterizing the performance of cognitive systems in the presence of interference and study of its behavior in the situations with the presence of random background noise
Nonequilibrium Enhances Adaptation Efficiency of Stochastic Biochemical Systems.
Directory of Open Access Journals (Sweden)
Chen Jia
Full Text Available Adaptation is a crucial biological function possessed by many sensory systems. Early work has shown that some influential equilibrium models can achieve accurate adaptation. However, recent studies indicate that there are close relationships between adaptation and nonequilibrium. In this paper, we provide an explanation of these two seemingly contradictory results based on Markov models with relatively simple networks. We show that as the nonequilibrium driving becomes stronger, the system under consideration will undergo a phase transition along a fixed direction: from non-adaptation to simple adaptation then to oscillatory adaptation, while the transition in the opposite direction is forbidden. This indicates that although adaptation may be observed in equilibrium systems, it tends to occur in systems far away from equilibrium. In addition, we find that nonequilibrium will improve the performance of adaptation by enhancing the adaptation efficiency. All these results provide a deeper insight into the connection between adaptation and nonequilibrium. Finally, we use a more complicated network model of bacterial chemotaxis to validate the main results of this paper.