Energy Technology Data Exchange (ETDEWEB)
Lu, Yunfan, E-mail: yunfanlu@yeah.net; Wang, Jun; Niu, Hongli
2015-06-12
An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model.
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas
2017-01-01
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. PMID:28190948
Realization of consensus of multi-agent systems with stochastically mixed interactions
Sun, Yongzheng; Li, Wang; Zhao, Donghua
2016-07-01
In this paper, we propose a new consensus model in which the interactions among agents stochastically switch between attraction and repulsion. Such a positive-and-negative mechanism is described by the white-noise-based coupling. Analytic criteria for the consensus and non-consensus in terms of the eigenvalues of the noise intensity matrix are derived, which provide a better understanding of the constructive roles of random interactions. Specifically, we discover a positive role of noise coupling that noise can accelerate the emergence of consensus. We find that the converging speed of the multi-agent network depends on the square of the second smallest eigenvalue of its graph Laplacian. The influence of network topologies on the consensus time is also investigated.
Analysis of bilinear stochastic systems
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Stochastic power system operation
Power, Michael
2010-01-01
This paper outlines how to economically and reliably operate a power system with high levels of renewable generation which are stochastic in nature. It outlines the challenges for system operators, and suggests tools and methods for meeting this challenge, which is one of the most fundamental since large scale power networks were instituted. The Ireland power system, due to its nature and level of renewable generation, is considered as an example in this paper.
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 ...
Stochastic sensing through covalent interactions
Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen
2013-03-26
A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.
Li, S.
2002-05-01
Taking advantage of the recent developments in groundwater modeling research and computer, image and graphics processing, and objected oriented programming technologies, Dr. Li and his research group have recently developed a comprehensive software system for unified deterministic and stochastic groundwater modeling. Characterized by a new real-time modeling paradigm and improved computational algorithms, the software simulates 3D unsteady flow and reactive transport in general groundwater formations subject to both systematic and "randomly" varying stresses and geological and chemical heterogeneity. The software system has following distinct features and capabilities: Interactive simulation and real time visualization and animation of flow in response to deterministic as well as stochastic stresses. Interactive, visual, and real time particle tracking, random walk, and reactive plume modeling in both systematically and randomly fluctuating flow. Interactive statistical inference, scattered data interpolation, regression, and ordinary and universal Kriging, conditional and unconditional simulation. Real-time, visual and parallel conditional flow and transport simulations. Interactive water and contaminant mass balance analysis and visual and real-time flux update. Interactive, visual, and real time monitoring of head and flux hydrographs and concentration breakthroughs. Real-time modeling and visualization of aquifer transition from confined to unconfined to partially de-saturated or completely dry and rewetting Simultaneous and embedded subscale models, automatic and real-time regional to local data extraction; Multiple subscale flow and transport models Real-time modeling of steady and transient vertical flow patterns on multiple arbitrarily-shaped cross-sections and simultaneous visualization of aquifer stratigraphy, properties, hydrological features (rivers, lakes, wetlands, wells, drains, surface seeps), and dynamically adjusted surface flooding area
Directory of Open Access Journals (Sweden)
K. Hacıefendioğlu
2012-04-01
Full Text Available The deconvolution effect of the near-fault earthquake ground motions on the stochastic dynamic response of tunnel-soil deposit interaction systems are investigated by using the finite element method. Two different earthquake input mechanisms are used to consider the deconvolution effects in the analyses: the standard rigid-base input and the deconvolved-base-rock input model. The Bolu tunnel in Turkey is chosen as a numerical example. As near-fault ground motions, 1999 Kocaeli earthquake ground motion is selected. The interface finite elements are used between tunnel and soil deposit. The mean of maximum values of quasi-static, dynamic and total responses obtained from the two input models are compared with each other.
Permanence of Stochastic Lotka-Volterra Systems
Liu, Meng; Fan, Meng
2017-04-01
This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.
Frequency Resonance in Stochastic Systems
Institute of Scientific and Technical Information of China (English)
钱敏; 张雪娟
2003-01-01
The phenomenon of frequency resonance, which is usually related to deterministic systems, is investigated in stochastic systems. We show that for those autonomous systems driven only by white noise, if the output power spectrum exhibits a nonzero peak frequency, then applying a periodic signel just on this noise-induced central frequency can also induce a resonance phenomenon, which we call the frequency stochastic resonance. The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.
Wang, Guochao; Wang, Jun
2017-01-01
We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system. The autocorrelation behaviors and the power-law scaling behaviors of return time series and VTRI series are investigated. Then, the complexity of VTRI series of the real markets and the proposed model is analyzed by Fuzzy entropy (FuzzyEn) and Lempel-Ziv complexity. In this process, we apply the cross-Fuzzy entropy (C-FuzzyEn) to study the asynchrony of pairs of VTRI series. The empirical results reveal that the proposed model has the similar complex behaviors with the actual markets and indicate that the proposed stock VTRI series analysis and the financial model are meaningful and feasible to some extent.
Stochastic genome-nuclear lamina interactions
Kind, Jop; van Steensel, Bas
2014-01-01
The nuclear lamina (NL) is thought to aid in the spatial organization of interphase chromosomes by providing an anchoring platform for hundreds of large genomic regions named lamina associated domains (LADs). Recently, a new live-cell imaging approach demonstrated directly that LAD-NL interactions are dynamic and in part stochastic. Here we discuss implications of these new findings and introduce Lamin A and BAF as potential modulators of stochastic LAD positioning. PMID:24717229
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...
Stochastic simulation in systems biology
Directory of Open Access Journals (Sweden)
Tamás Székely Jr.
2014-11-01
There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Stochastic waves in a Brusselator model with nonlocal interaction.
Biancalani, Tommaso; Galla, Tobias; McKane, Alan J
2011-08-01
We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically induced patterns.
Stochastic simulation in systems biology.
Székely, Tamás; Burrage, Kevin
2014-11-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Interactive macroeconomics stochastic aggregate dynamics with heterogeneous and interacting agents
Di Guilmi, Corrado
2017-01-01
One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of macroeconomic modelling a...
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, m
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, m
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...
Symmetry reduction for stochastic hybrid systems
Bujorianu, L.M.; Katoen, J.P.
2009-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. We first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Then, we genera
Symmetry Reduction For Stochastic Hybrid Systems
Bujorianu, L.M.; Katoen, J.P.
2008-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. To that end, we first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Th
Stochastic averaging of quasi-Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Approximation scheme based on effective interactions for stochastic gene regulation
Ohkubo, Jun
2010-01-01
Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme for dealing with the stochasticity of the gene regulatory systems. Using an effective interaction concept, original master equations can be reduced to simpler master equations, which can be solved analytically. We apply the approximation scheme to self-regulating systems with monomer or dimer interactions, and a two-gene system with an exclusive switch. The approximation scheme can recover bistability of the exclusive switch adequately.
Inference of a nonlinear stochastic model of the cardiorespiratory interaction
Smelyanskiy, V N; Stefanovska, A; McClintock, P V E
2005-01-01
A new technique is introduced to reconstruct a nonlinear stochastic model of the cardiorespiratory interaction. Its inferential framework uses a set of polynomial basis functions representing the nonlinear force governing the system oscillations. The strength and direction of coupling, and the noise intensity are simultaneously inferred from a univariate blood pressure signal, monitored in a clinical environment. The technique does not require extensive global optimization and it is applicable to a wide range of complex dynamical systems subject to noise.
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...
Stochastic stabilization analysis of networked control systems
Institute of Scientific and Technical Information of China (English)
Ma Changlin; Fang Huajing
2007-01-01
Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.
Stochastic heterogeneous interaction promotes cooperation in spatial prisoner's dilemma game.
Directory of Open Access Journals (Sweden)
Ping Zhu
Full Text Available Previous studies mostly investigate player's cooperative behavior as affected by game time-scale or individual diversity. In this paper, by involving both time-scale and diversity simultaneously, we explore the effect of stochastic heterogeneous interaction. In our model, the occurrence of game interaction between each pair of linked player obeys a random probability, which is further described by certain distributions. Simulations on a 4-neighbor square lattice show that the cooperation level is remarkably promoted when stochastic heterogeneous interaction is considered. The results are then explained by investigating the mean payoffs, the mean boundary payoffs and the transition probabilities between cooperators and defectors. We also show some typical snapshots and evolution time series of the system. Finally, the 8-neighbor square lattice and BA scale-free network results indicate that the stochastic heterogeneous interaction can be robust against different network topologies. Our work may sharpen the understanding of the joint effect of game time-scale and individual diversity on spatial games.
Stochastic heterogeneous interaction promotes cooperation in spatial prisoner's dilemma game.
Zhu, Ping; Wei, Guiyi
2014-01-01
Previous studies mostly investigate player's cooperative behavior as affected by game time-scale or individual diversity. In this paper, by involving both time-scale and diversity simultaneously, we explore the effect of stochastic heterogeneous interaction. In our model, the occurrence of game interaction between each pair of linked player obeys a random probability, which is further described by certain distributions. Simulations on a 4-neighbor square lattice show that the cooperation level is remarkably promoted when stochastic heterogeneous interaction is considered. The results are then explained by investigating the mean payoffs, the mean boundary payoffs and the transition probabilities between cooperators and defectors. We also show some typical snapshots and evolution time series of the system. Finally, the 8-neighbor square lattice and BA scale-free network results indicate that the stochastic heterogeneous interaction can be robust against different network topologies. Our work may sharpen the understanding of the joint effect of game time-scale and individual diversity on spatial games.
Quadratic stabilization for uncertain stochastic systems
Institute of Scientific and Technical Information of China (English)
Jun'e FENG; Weihai ZHANG
2005-01-01
This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
Stochastic versus deterministic systems of differential equations
Ladde, G S
2003-01-01
This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/flu
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...
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...
Quantitative sociodynamics stochastic methods and models of social interaction processes
Helbing, Dirk
1995-01-01
Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the log...
Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes
Helbing, Dirk
2010-01-01
This new edition of Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioral changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics and mathematics, but they have very often proven their explanatory power in chemistry, biology, economics and the social sciences as well. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces important concepts from nonlinear dynamics (e.g. synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches, a fundamental dynamic model is obtained, which opens new perspectives in the social sciences. It includes many established models a...
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation uncerta
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation uncerta
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 hyperfine interactions modeling library-Version 2
Zacate, Matthew O.; Evenson, William E.
2016-02-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized. The original version of SHIML constructed and solved Blume matrices for methods that measure hyperfine interactions of nuclear probes in a single spin state. Version 2 provides additional support for methods that measure interactions on two different spin states such as Mössbauer spectroscopy and nuclear resonant scattering of synchrotron radiation. Example codes are provided to illustrate the use of SHIML to (1) generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A22 can be neglected and (2) generate Mössbauer spectra for polycrystalline samples for pure dipole or pure quadrupole transitions.
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
Complexity and synchronization in stochastic chaotic systems
Son Dang, Thai; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo
2016-02-01
We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.
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 introduct......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...
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique...... applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings....
Stochastic Physics, Complex Systems and Biology
Qian, Hong
2012-01-01
In complex systems, the interplay between nonlinear and stochastic dynamics gives rise to an evolution process in Darwinian sense with punctuated equilibrium, random "mutations" and "adaptations". The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Epigenetic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a framework.
Stochastic system identification in structural dynamics
Safak, Erdal
1988-01-01
Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.
Parametric resonance and particle stochastic interactions with a periodic medium
Pinheiro, Mario J
2015-01-01
A non-markovian stochastic model shows the emergence of structures in the medium, a self-organization characterized by a relationship between particle's energy, driven frequency $\\omega$ and a frequency of interaction with the medium $\
Stochastic relations foundations for Markov transition systems
Doberkat, Ernst-Erich
2007-01-01
Collecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
equations are expressed in terms of stochastic differential equations. From a theoretical viewpoint the techniques for experimental design, parameter estimation and model validation are considered. From the practical viewpoint emphasis is put on how this methods can be used to construct models adequate...
Synchronization of noisy systems by stochastic signals
Energy Technology Data Exchange (ETDEWEB)
Neiman, A.; Schimansky-Geier, L.; Moss, F. [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Schimansky-Geier, L. [Institute of Physics, Humboldt University at Berlin, Invalidenstrasse 110, D-10115 Berlin (Germany); Shulgin, B.; Collins, J.J. [Center for BioDynamics and Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215 (United States)
1999-07-01
We study, in terms of synchronization, the {ital nonlinear response} of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level{emdash}this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train. {copyright} {ital 1999} {ital The American Physical Society}
Interacting Stochastic Processes: From Viciousness to Caging to Force Chains
Xu, Shiliyang
This thesis documents a quest to develop and study several novel interacting stochastic processes. As for the first example, we generalize a system of vicious random walkers in which the only interaction between any two random walkers is that when they intersect, both walkers are annihilated. We define a system of N vicious accelerating walkers with each walker undergoing random acceleration and compute the survival probability distribution for this system. We also define and study a system of N vicious Levy flights in which any two Levy flights crossing one another annihilate each other. The average mean-squared displacement of a Levy flight is not proportional to time, but scales with what is known as the Levy index divided by two. In both cases, vicious accelerating walkers and vicious Levy flights, we are motivated by ultimately generalizing our understanding of Gaussian random matrices via non-Markovian and non-Gaussian extensions respectively. Moreover, inspired by recent experiments on periodically sheared colloids at low densities, we define and investigate several new contact processes, or interacting stochastic processes, with conserved particle number and three-or-more-body interactions. We do so to characterize the periodically sheared colloidal system at higher densities. We find two new dynamical phase transitions between an active phase, where some fraction of the colloids are always being displaced from their position at the beginning and end of each shear cycle, and an inactive phase in which all colloids return to their initial positions at the end of each shear cycle. One of the transitions is discontinuous, while the second, which is due to a caging, or crowding, effect at high densities, appears to be continuous and in a new universality from what is known as conserved directed percolation. The latter transition may have implications for the onset of glassiness in dense, particulate systems. In addition, this thesis also includes analysis of
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.
Luo, Albert C J
2011-01-01
In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.
[Deterministic and stochastic identification of neurophysiologic systems].
Piatigorskiĭ, B Ia; Kostiukov, A I; Chinarov, V A; Cherkasskiĭ, V L
1984-01-01
The paper deals with deterministic and stochastic identification methods applied to the concrete neurophysiological systems. The deterministic identification was carried out for the system: efferent fibres-muscle. The obtained transition characteristics demonstrated dynamic nonlinearity of the system. Identification of the neuronal model and the "afferent fibres-synapses-neuron" system in mollusc Planorbis corneus was carried out using the stochastic methods. For these purpose the Wiener method of stochastic identification was expanded for the case of pulse trains as input and output signals. The weight of the nonlinear component in the Wiener model and accuracy of the model prediction were quantitatively estimated. The results obtained proves the possibility of using these identification methods for various neurophysiological systems.
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Vector Lyapunov Functions for Stochastic Interconnected Systems
Boussalis, D.
1985-01-01
Theoretical paper presents set of sufficient conditions for asymptotic and exponential stability with probability 1 for class of stochastic interconnected systems. Theory applicable to complicated, large-scale mechanical or electrical systems, and, for several design problems, it reduces computational difficulty by relating stability criteria to fundamental structural features of system.
Vector Lyapunov Functions for Stochastic Interconnected Systems
Boussalis, D.
1985-01-01
Theoretical paper presents set of sufficient conditions for asymptotic and exponential stability with probability 1 for class of stochastic interconnected systems. Theory applicable to complicated, large-scale mechanical or electrical systems, and, for several design problems, it reduces computational difficulty by relating stability criteria to fundamental structural features of system.
Stochastic description for open quantum systems
Calzetta, E A; Verdaguer, E; Calzetta, Esteban; Roura, Albert; Verdaguer, Enric
2000-01-01
A linear open quantum system consisting of a harmonic oscillator coupled linearly to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in thermal equilibrium. Using the influence functional formalism a formal Langevin equation can be introduced to describe the system's fully quantum properties even beyond the semiclassical regime. It is shown that the reduced Wigner function for the system is exactly the formal distribution function resulting from averaging both over the initial conditions and the stochastic source of the formal Langevin equation. The master equation for the reduced density matrix is then obtained in the same way a Fokker-Planck equation can always be derived from a Langevin equation characterizing a stochastic process. We also show that the quantum correlation functions for the system can be deduced within the stochastic description provided by the Langevin equation. It is emphasized that when the s...
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.
Robustness analysis of stochastic biochemical systems.
Ceska, Milan; Safránek, David; Dražan, Sven; Brim, Luboš
2014-01-01
We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
Conformal invariance in conditioned stochastic particle systems
Schütz, Gunter M.
2017-08-01
We consider space-time correlations in generic one-dimensional stochastic interacting particle systems with short-range interactions that undergo a fluctuation with an atypically activity of particle jumps or reactions or spin flips. We briefly review the approach in the framework of the quantum Hamiltonian formalism and present examples where the dynamics during such large fluctuations is governed not by the typical stationary dynamics, but by ballistic universality classes with dynamical exponent z=1 that are described unitary conformally invariant field theories with central charge c. For reaction-diffusion and spin flip dynamics we identify critical points (a) in the Ising universality class with c=1/2 , and (b) in the universality class of the three-states Potts model with c=4/5 . For the Ising universality class we obtain a universal scaling form for the generating function of cumulants of the jump activity. For repulsive driven diffusive systems with one conservation law the regime of an atypically high current or hopping activity is generically conformally invariant with central charge c=1 .
Size and stochasticity in irrigated social-ecological systems
Puy, Arnald; Muneepeerakul, Rachata; Balbo, Andrea L.
2017-01-01
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. PMID:28266656
Impulsive control of stochastic system under the sense of stochastic asymptotical stability
Institute of Scientific and Technical Information of China (English)
Niu Yu-Jun; Ma Ge
2010-01-01
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterimpulsive control method,and numerical simulations are employed to verify the feasibility of this method.
Institute of Scientific and Technical Information of China (English)
林敏; 张美丽; 黄咏梅
2011-01-01
The interaction of a coupled system and an external force is analyzed.The method of controlling stochastic energetic resonance is proposed from the viewpoint of work done and energy.According to the stochastic dynamics described by two-dimensional coupled Langevin equation, the thermodynamic relations of coupled systems based on single stochastic trajectories are established using microcosmic dynamics and macroscopic thermodynamic methods.By adjusting the periodic external force acting upon the control system, the work that is done on the coupled system by the input force acting on a controlled system and energy conversion relations are quantitatively characterized.The results show that the interaction of a coupled system, an input force and noise can be controlled by the control signal, and stochastic energetic resonance in a coupled system can be effectively controlled by the control signal.%分析了耦合系统与外界作用力的交互作用,从做功与能量的角度提出了控制随机能量共振的方法.根据二维耦合Langevin方程的随机动力学特性,采用微观动力学和宏观热力学方法,建立了基于单一随机轨线的耦合系统的热力学关系.通过调节施加于控制系统的周期性外力,定量刻画了作用于被控系统的输入力对耦合系统做功的大小与能量转换关系.结果表明,控制信号能控制耦合系统与输入力和噪声之间的相互作用,能有效地控制耦合系统的随机能量共振.
Stochastic Mode-Reduction in Models with Conservative Fast Sub-Systems
Jain, Ankita; Timofeyev, Ilya; Vanden-Eijnden, Eric
2014-01-01
A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast sub-system in an energy-conserving fashion. Since the stochastic terms only affect the slow variables, the fast-subsystem evolves deterministically on a sphere of constant energy. However, in the full model the radius of the sphere slowly changes due to the...
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
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.
Analysis of bilinear stochastic systems. [involving multiplicative noise processes
Willsky, A. S.; Marcus, S. I.; Martin, D. N.
1974-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Stochastic Process Analysis of Interactive Discourse in Early Counseling Interviews.
Friedlander, Myrna L.; Phillips, Susan D.
1984-01-01
Examined patterns of interactive discourse to suggest how client and counselor establish a working alliance in their early interviews. Based on classification of 312 conversational turns from 14 dyads, a stochastic analysis was conducted. Results showed the sequences of talk were highly stable and predictable. (JAC)
Stochastic Approaches to Interactive Multi-Criteria Optimization Problems
1986-01-01
A stochastic approach to the development of interactive algorithms for multicriteria optimization is discussed in this paper. These algorithms are based on the idea of a random search and the use of a decision-maker who can compare any two decisions. The questions of both theoretical analysis (proof of convergence, investigation of stability) and practical implementation of these algorithms are discussed.
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...
On the Stability of Bilinear Stochastic Systems
1988-08-01
d’Equations Differentielles Stochastiques Lineaires", Journees Stabilite Asymptotique des Systemes Differentiels a Perturbation Aleatoire. CNRS, 1986. [3...for the Lyapunov numbers associated with this equation are given. Bilinear noise models are, after linear ones, the second simplest case of stochastic...give a condition for the stability with probability one of the d-dimensional Ito equation which describes the behavior of such a system dYs = AYs ds
Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions
2014-10-09
motions and other stochastic processes. For the control of both continuous time and discrete time finite dimensional linear systems with quadratic...problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...2010 30-Jun-2014 Approved for Public Release; Distribution Unlimited Final Report: Optimal Control of Stochastic Systems Driven by Fractional Brownian
Influence of stochastic perturbation on prey-predator systems.
Rudnicki, Ryszard; Pichór, Katarzyna
2007-03-01
We analyse the influence of various stochastic perturbations on prey-predator systems. The prey-predator model is described by stochastic versions of a deterministic Lotka-Volterra system. We study long-time behaviour of both trajectories and distributions of the solutions. We indicate the differences between the deterministic and stochastic models.
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).
Directory of Open Access Journals (Sweden)
Fei Long
2013-01-01
Full Text Available For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.
Mathematical model for hit phenomena as stochastic process of interactions of human interactions
Ishii, Akira; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshda, Narihiko
2011-01-01
Mathematical model for hit phenomena in entertainments in the society is presented as stochastic process of interactions of human dynamics. The model use only the time distribution of advertisement budget as input and the words of mouth (WOM) as posting in the social network system is used as the data to compare with the calculated results. The unit of time is daily. The WOM distribution in time is found to be very close to the residue distribution in time. The calculations for Japanese motion picture market due to the mathematical model agree very well with the actual residue distribution in time.
Fixed Points for Stochastic Open Chemical Systems
Malyshev, V A
2011-01-01
In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for Boltzman equation. Classical chemical kinetics and chemical thermodynamics are obtained as some scaling limits in the models, introduced below. In the second part of this paper we specify some simple class of open chemical reaction systems, where one can still prove the existence of attracting fixed points. For example, Michaelis\\tire Menten kinetics belongs to this class. At the end we present a simplest possible model of the biological network. It is a network of networks (of closed chemical reaction systems, called compartments), so that the only source of nonreversibility is the matter exchange (transport) with the environment and between the compartments. Keywords: chemical kinetics, chemical thermodynamics, Kac model, mathematical biology
Conditional reversibility in nonequilibrium stochastic systems
Bonança, Marcus V. S.; Jarzynski, Christopher
2016-02-01
For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate σ , is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, -σ , where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.
Modelling Coagulation Systems: A Stochastic Approach
Ryazanov, V V
2011-01-01
A general stochastic approach to the description of coagulating aerosol system is developed. As the object of description one can consider arbitrary mesoscopic values (number of aerosol clusters, their size etc). The birth-and-death formalism for a number of clusters can be regarded as a partial case of the generalized storage model. An application of the storage model to the number of monomers in a cluster is discussed.
Stochastic measurements and systems implications
Collins, J. L.; Greene, R. R.
1985-06-01
The U.S. Navy is defining the baseline performance of the current SSN ASW suite in the Arctic operating environment. This suite includes the AN/BQQ-5 sonar suit (including the Towed Array, the sphere and other sensor and processor sub-systems), communications subsystems and weapon systems (Mk 48 and ADCAP). An effective acoustic measurement program in the Arctic must support the evaluation of how well the different subsystems are able to carry out their assigned functions. Unique aspects of the operating environment in the Arctic include unusual noise properties, unusual transmission effects and an unusual sea surface. This report addresses those acoustic transmission effects which affect system performance due to fluctuations or spreads in the acoustic field space, angle time and frequency.
Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer-van der Pol system
Institute of Scientific and Technical Information of China (English)
Zhang Ying; Xu Wei; Fang Tong; Xu Xu-Lin
2007-01-01
In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol (BVP for short) system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter.The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.
Robust stability of uncertain neutral linear stochastic differential delay system
Institute of Scientific and Technical Information of China (English)
JIANG Ming-hui; SHEN Yi; LIAO Xiao-xin
2007-01-01
The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.
Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics
Institute of Scientific and Technical Information of China (English)
Xin Yu; Na Duan
2009-01-01
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Stochastic Models of Polymer Systems
2016-01-01
field limit of a dynamical model for polymer systems, Science China Mathematics , (11 2012): 0. doi: TOTAL: 1 Number of Non Peer-Reviewed Conference...4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education , Research and Engineering...undergraduates funded by your agreement who graduated during this period and will receive scholarships or fellowships for further studies in science
Stochastic seismic tomography by interacting Markov chains
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-10-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches, they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high-dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case, the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on importance resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non-linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper, the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a simulated annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet-based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Stochastic seismic tomography by interacting Markov chains
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-07-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on Importance Resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a Simulated Annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Li, Juan
2012-01-01
In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations developed by Pardoux and Zhang [17]. The value function is shown to be the viscosity solution to the associated Hamilton-Jacobi-Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. The method of stochastic "backward semigroups" introduced by Peng [18] is adapted to our context.
A Multiobjective Optimization Framework for Stochastic Control of Complex Systems
Energy Technology Data Exchange (ETDEWEB)
Malikopoulos, Andreas [ORNL; Maroulas, Vasileios [ORNL; Xiong, Professor Jie [The University of Tennessee
2015-01-01
This paper addresses the problem of minimizing the long-run expected average cost of a complex system consisting of subsystems that interact with each other and the environment. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems, and we show that the control policy yielding the Pareto optimal solution is an optimal control policy that minimizes the average cost criterion for the entire system. For practical situations with constraints consistent to those we study here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems.
System Optimization Using a Parallel Stochastic Approach
Directory of Open Access Journals (Sweden)
ZAPLATILEK, K.
2013-05-01
Full Text Available This paper describes an original stochastic algorithm based on a parallel approach. The algorithm is suitable especially for a real technical system optimization. A few independent pseudorandom generators are used. They generate independent variable vectors along all of the optimized system axes. Local optimal values are used to define a final pseudorandom generator with a narrower interval around the global optimum. Theoretical foundations are introduced and a few practical experiments are presented. The described method is also suitable for the quality classification of the pseudorandom generators using the selected RGB color scheme. Main advantages of this approach are discussed. The algorithm was developed in the MATLAB environment.
Effect of signal modulating noise in bistable stochastic dynamical systems
Institute of Scientific and Technical Information of China (English)
肖方红; 闫桂荣; 张新武
2003-01-01
The effect of signal modulating noise in bistable stochastic dynamical systems is studied.The concept of instan taneous steady state is proposed for bistable dynamical systems.By making a dynamical analysis of bistable stochastic systems,we find that global and local effect of signal modulating noise as well as stochastic resonance can occur in bistable dynamical systems on which both a weak sinusoidal signal and noise are forced.The effect is demonstrated by numerical simulation.
Approximation Methods in Stochastic Max-Plus Systems
Safaei Farahani, S.
2012-01-01
Stochastic max-plus systems belong to a special class of discrete-event systems. This class consists of systems with synchronization but no choice and the models of such systems are defined using the operators maximization and addition. Stochastic max-plus systems can be further extended
Stochastic dynamics of interacting haematopoietic stem cell niche lineages.
Directory of Open Access Journals (Sweden)
Tamás Székely
2014-09-01
Full Text Available Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.
Stochastic stability properties of jump linear systems
Feng, Xiangbo; Loparo, Kenneth A.; Ji, Yuandong; Chizeck, Howard J.
1992-01-01
Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.
System Entropy Measurement of Stochastic Partial Differential Systems
Directory of Open Access Journals (Sweden)
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.
Robust stabilization of stochastic systems based on the LQ controller
Institute of Scientific and Technical Information of China (English)
Jundong BAO; Feiqi DENG; Qi LUO
2005-01-01
The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with.For the uncertain stochastic systems,we have designed an optimal controller which guarantees the exponential stability of the system.Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic(LQ) optimal control law.And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.
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...
A validation study of a stochastic model of human interaction
Burchfield, Mitchel Talmadge
The purpose of this dissertation is to validate a stochastic model of human interactions which is part of a developmentalism paradigm. Incorporating elements of ancient and contemporary philosophy and science, developmentalism defines human development as a progression of increasing competence and utilizes compatible theories of developmental psychology, cognitive psychology, educational psychology, social psychology, curriculum development, neurology, psychophysics, and physics. To validate a stochastic model of human interactions, the study addressed four research questions: (a) Does attitude vary over time? (b) What are the distributional assumptions underlying attitudes? (c) Does the stochastic model, {-}N{intlimitssbsp{-infty}{infty}}varphi(chi,tau)\\ Psi(tau)dtau, have utility for the study of attitudinal distributions and dynamics? (d) Are the Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein theories applicable to human groups? Approximately 25,000 attitude observations were made using the Semantic Differential Scale. Positions of individuals varied over time and the logistic model predicted observed distributions with correlations between 0.98 and 1.0, with estimated standard errors significantly less than the magnitudes of the parameters. The results bring into question the applicability of Fisherian research designs (Fisher, 1922, 1928, 1938) for behavioral research based on the apparent failure of two fundamental assumptions-the noninteractive nature of the objects being studied and normal distribution of attributes. The findings indicate that individual belief structures are representable in terms of a psychological space which has the same or similar properties as physical space. The psychological space not only has dimension, but individuals interact by force equations similar to those described in theoretical physics models. Nonlinear regression techniques were used to estimate Fermi-Dirac parameters from the data. The model explained a high degree
Conserved quantities and symmetries related to stochastic Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Shang Mei; Mei Feng-Xiang
2007-01-01
In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail.Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether's theorem.
Stochastic thermodynamics for delayed Langevin systems.
Jiang, Huijun; Xiao, Tiejun; Hou, Zhonghuai
2011-06-01
We discuss stochastic thermodynamics (ST) for delayed Langevin systems in this paper. By using the general principles of ST, the first-law-like energy balance and trajectory-dependent entropy s(t) can be well defined in a way that is similar to that in a system without delay. Because the presence of time delay brings an additional entropy flux into the system, the conventional second law (Δs(tot))≥0 no longer holds true, where Δs(tot) denotes the total entropy change along a stochastic path and (·) stands for the average over the path ensemble. With the help of a Fokker-Planck description, we introduce a delay-averaged trajectory-dependent dissipation functional η[χ(t)] which involves the work done by a delay-averaged force F(x,t) along the path χ(t) and equals the medium entropy change Δs(m)[x(t)] in the absence of delay. We show that the total dissipation functional R=Δs+η, where Δs denotes the system entropy change along a path, obeys (R)≥0, which could be viewed as the second law in the delayed system. In addition, the integral fluctuation theorem (e(-R))=1 also holds true. We apply these concepts to a linear Langevin system with time delay and periodic external force. Numerical results demonstrate that the total entropy change (Δs(tot)) could indeed be negative when the delay feedback is positive. By using an inversing-mapping approach, we are able to obtain the delay-averaged force F(x,t) from the stationary distribution and then calculate the functional R as well as its distribution. The second law (R)≥0 and the fluctuation theorem are successfully validated.
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.
2012-04-17
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.
Institute of Scientific and Technical Information of China (English)
Ma Shao-Juan; Xu Wei; Li Wei; Fang Tong
2006-01-01
The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter.Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.
Stochastic bifurcations in a prototypical thermoacoustic system.
Gopalakrishnan, E A; Tony, J; Sreelekha, E; Sujith, R I
2016-08-01
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.
Stochastic bifurcations in a prototypical thermoacoustic system
Gopalakrishnan, E. A.; Tony, J.; Sreelekha, E.; Sujith, R. I.
2016-08-01
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.
Time-ordered product expansions for computational stochastic system biology.
Mjolsness, Eric
2013-06-01
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.
Stochastic resonance enhanced by dichotomic noise in a bistable system
Energy Technology Data Exchange (ETDEWEB)
Rozenfeld, Robert [Institute for Physics, Humboldt University at Berlin, D-10115, Berlin, (Germany); Neiman, Alexander [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Schimansky-Geier, Lutz [Institute for Physics, Humboldt University at Berlin, D-10115, Berlin, (Germany)
2000-09-01
We study linear responses of a stochastic bistable system driven by dichotomic noise to a weak periodic signal. We show that the effect of stochastic resonance can be greatly enhanced in comparison with the conventional case when dichotomic forcing is absent, that is, both the signal-to-noise ratio and the spectral power amplification reach much greater values than in the standard stochastic resonance setup. (c) 2000 The American Physical Society.
Towards a General Theory of Stochastic Hybrid Systems
Bujorianu, L.M.; Lygeros, J.; Bujorianu, M. C.
2008-01-01
In this paper we set up a mathematical structure, called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a mixing mechanism of stochastic processes, introduced by Meyer. We prove that Markov strings are strong Markov processes with the cadlag property. We then show how a very general class of stochastic hybrid processes can be embedded in the framework of Markov strings. This class,...
Stochastic impulsive control for the stabilization of Lorenz system
Institute of Scientific and Technical Information of China (English)
Wang Liang; Zhao Rui; Xu Wei; Zhang Ying
2011-01-01
This paper derives some sufficient conditions for the stabilization of Lorenz system with stochastic impulsive control. The estimate of the upper bound of impulse interval for asymptotically stable control is obtained. Some differences between the system with stochastic impulsive control and with deterministic impulsive control are presented. Computer simulation is given to show the effectiveness of the proposed method.
Waiting time distribution for continuous stochastic systems.
Gernert, Robert; Emary, Clive; Klapp, Sabine H L
2014-12-01
The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012)]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.
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.
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Energy Technology Data Exchange (ETDEWEB)
Branicki, M., E-mail: branicki@cims.nyu.edu [Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University (United States); Majda, A.J. [Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University (United States)
2013-05-15
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
Stochastic Local Interaction (SLI) model: Bridging machine learning and geostatistics
Hristopulos, Dionissios T.
2015-12-01
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to improve computational efficiency. SLI combines geostatistics and machine learning with ideas from statistical physics and computational geometry. It is based on a joint probability density function defined by an energy functional which involves local interactions implemented by means of kernel functions with adaptive local kernel bandwidths. SLI is expressed in terms of an explicit, typically sparse, precision (inverse covariance) matrix. This representation leads to a semi-analytical expression for interpolation (prediction), which is valid in any number of dimensions and avoids the computationally costly covariance matrix inversion.
Stochastic models for uncertain flexible systems
Curtain, R.F.; Kotelenez, P.
1987-01-01
If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexib
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1980-01-01
Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Qichun; Zhou, Jinglin; Wang, Hong; Chai, Tianyou
2016-08-31
In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.
Towards a General Theory of Stochastic Hybrid Systems
Bujorianu, L.M.; Lygeros, J.; Bujorianu, M.C.
2008-01-01
In this paper we set up a mathematical structure, called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a mixing mechanism of stochastic processes, introduced by Meyer. We prove that Mark
Toward a General Theory of Stochastic Hybrid Systems
Bujorianu, L.M.; Lygeros, J.; Blom, H.A.P.; Lygeros, J.
2006-01-01
In this chapter we set up a mathematical structure, called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a mixing mechanism of stochastic processes, introduced by Meyer. We prove that Ma
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Consistency of global total least squares in stochastic system identification
C. Heij (Christiaan); W. Scherrer
1995-01-01
textabstractGlobal total least squares has been introduced as a method for the identification of deterministic system behaviours. We analyse this method within a stochastic framework, where the observed data are generated by a stationary stochastic process. Conditions are formulated so that the meth
Stochastic bifurcation in a driven laser system: experiment and theory.
Billings, Lora; Schwartz, Ira B; Morgan, David S; Bollt, Erik M; Meucci, Riccardo; Allaria, Enrico
2004-08-01
We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class- B laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior, or noise-induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius-Perron operator [L. Billings et al., Phys. Rev. Lett. 88, 234101 (2002)] to a model of the experimental system. Our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment. In quantifying the stochastic bifurcation, we have computed a transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius-Perron operator. This mechanism depends on both the standard deviation of the noise and the global topology of the system. Our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise-induced chaos in both theory and experiment.
Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Krishnan Balachandran
2008-12-01
Full Text Available In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.
Random-order fractional bistable system and its stochastic resonance
Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia
2017-01-01
In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.
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).
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.
Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay
Sakthivel, R.; Ganesh, R.; Suganya, S.
2012-12-01
The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
Bounded stabilisation of stochastic port-Hamiltonian systems
Satoh, Satoshi; Saeki, Masami
2014-08-01
This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances.
On the stochastic behaviors of locally confined particle systems
Energy Technology Data Exchange (ETDEWEB)
Li, Yao, E-mail: yaoli@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2015-07-15
We investigate a class of Hamiltonian particle systems and their stochastic behaviors. Using both rigorous proof and numerical simulations, we show that the geometric configuration can qualitatively change key statistical characteristics of the particle system, which are expected to be retained by stochastic modifications. In particular, whether a particle system has an exponential mixing rate or a polynomial mixing rate depends on whether the geometric setting allows a slow particle being reached by adjacent fast particles.
Optimal inspection and maintenance for stochastically deteriorating systems
Dagg, R.A.
1999-01-01
This thesis concerns the optimisation of maintenance and inspection for stochastically deteriorating systems. The motivation for this thesis is the problem of determining condition based maintenance policies, for systems whose degradation may be modelled by a continuous time stochastic process. Our emphasis is mainly on using the information gained from inspecting the degradation to determine efficient maintenance and inspection policies. The system we shall consider is one in which the degra...
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Stochastic uncertainty analysis for unconfined flow systems
Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming
2006-01-01
A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen-Loeve decomposition-based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen-Loeve decomposition, polynomial expansion, and perturbation methods. The random log-transformed hydraulic conductivity field (InKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of InKS- Next, head h is decomposed as a perturbation expansion series ??A(m), where A(m) represents the mth-order head term with respect to the standard deviation of InKS. Then A(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients Ai1,i2(m)...,im are deterministic and solved sequentially from low to high expansion orders using MODFLOW-2000. Finally, the statistics of head and flux are computed using simple algebraic operations on Ai1,i2(m)...,im. A series of numerical test results in 2-D and 3-D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique. Copyright 2006 by the American Geophysical Union.
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.
Computational Methods for Predictive Simulation of Stochastic Turbulence Systems
2015-11-05
AFRL-AFOSR-VA-TR-2015-0363 Computational Methods for Predictive Simulation of Stochastic Turbulence Systems Catalin Trenchea UNIVERSITY OF PITTSBURGH...STOCHASTIC TURBULENCE SYSTEMS AFOSR GRANT FA 9550-12-1-0191 William Layton and Catalin Trenchea Department of Mathematics University of Pittsburgh...During Duration of Grant Nan Jian Graduate student, Univ . of Pittsburgh (currently Postdoc at FSU) Sarah Khankan Graduate student, Univ . of Pittsburgh
EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY HYBRID SYSTEMS WITH MARKOVIAN SWITCHING
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper deals with the problem of norm bounds for the solutions of stochastic hybrid systems with Markovian switching and time delay. Based on Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach, mean square exponential estimates for the solutions of this class of linear stochastic hybrid systems are derived. Finally, An example is illustrated to show the applicability and effectiveness of our method.
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.
Quantum stopping times stochastic integral in the interacting Fock space
Energy Technology Data Exchange (ETDEWEB)
Kang, Yuanbao, E-mail: kangyuanb@163.com [College of Mathematics Science, Chong Qing Normal University, Chongqing 400047 (China)
2015-08-15
Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L{sup 2}(ℝ{sup +}), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L{sup 2}(ℝ{sup +}) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ{sub τ]} ⊗ Γ{sub [τ}, where Γ{sub τ]} and Γ{sub [τ} stand for the part “before τ” and the part “after τ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.
Institute of Scientific and Technical Information of China (English)
Shu-jun Liu; Ji-feng Zhang; Zhong-ping Jiang
2008-01-01
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical)stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process
Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko
2012-06-01
A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
Oceanic stochastic parametrizations in a seasonal forecast system
Andrejczuk, M; Juricke, S; Palmer, T N; Weisheimer, A; Zanna, L
2015-01-01
We study the impact of three stochastic parametrizations in the ocean component of a coupled model, on forecast reliability over seasonal timescales. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the Stochastically Perturbed Parametrization Tendency (SPPT) scheme - which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely the western boundary currents and the Southern Ocean. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error. Whilst there are good grounds for implementing stochastic schemes in ocean models, our results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.
Stochastic differential equations and a biological system
DEFF Research Database (Denmark)
Wang, Chunyan
1994-01-01
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......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......, Milstein and Runge-Kutta methods are used. Because of the specific feature of the model for the growth process, that its solution does not exist in the general sense, we combine these numerical integration methods with a transformation technique, and the solutions are derived in the Ito sense...
On the equivalence between stochastic baker's maps and two-dimensional spin systems
Lindgren, K.
2010-05-01
We show that there is a class of stochastic bakers transformations that is equivalent to the class of equilibrium solutions of two-dimensional spin systems with finite interaction. The construction is such that the equilibrium distribution of the spin lattice is identical to the invariant measure in the corresponding bakers transformation. We illustrate the equivalence by deriving two stochastic bakers maps representing the Ising model at a temperature above and below the critical temperature, respectively. A calculation of the invariant measure and the free energy in the baker system is then shown to be in agreement with analytic results of the two-dimensional Ising model.
STOCHASTIC HOPF BIFURCATION IN QUASI-INTEGRABLE-HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Chunbiao
2004-01-01
A new procedure is developed to study the stochastic Hopf bifurcation in quasiintegrable-Hamiltonian systems under the Gaussian white noise excitation. Firstly, the singular boundaries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system's energy levels with respect to the stochastic averaging method. Secondly, the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones. Lastly, a quasi-integrableHamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure.Moreover, simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure. It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system's parameters. Therefore, one can see that the numerical results are consistent with the theoretical predictions.
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.
Balibrea-Iniesta, Francisco; Lopesino, Carlos; Wiggins, Stephen; Mancho, Ana M.
2016-12-01
In this paper, we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport.
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.
Attractors for stochastic lattice dynamical systems with a multiplicative noise
Institute of Scientific and Technical Information of China (English)
Tomás CARABALLO; Kening LU
2008-01-01
In this paper,we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction,a dissipative nonlinear reaction term,and multiplicative white noise at each node.We prove the existence of a compact global random attractor which,pulled back,attracts tempered random bounded sets.
CISM Course on Analysis and Estimation of Stochastic Mechanical Systems
Wedig, Walter
1988-01-01
This book summarizes the developments in stochastic analysis and estimation. It presents novel applications to practical problems in mechanical systems. The main aspects of the course are random vibrations of discrete and continuous systems, analysis of nonlinear and parametric systems, stochastic modelling of fatigue damage, parameter estimation and identification with applications to vehicle road systems and process simulations by means of autoregressive models. The contributions will be of interest to engineers and research workers in industries and universities who want first hand information on present trends and problems in this topical field of engineering dynamics.
Optimal Vaccination in a Stochastic Epidemic Model of Two Non-Interacting Populations
2015-02-17
RESEARCH ARTICLE Optimal Vaccination in a Stochastic Epidemic Model of Two Non-Interacting Populations Edwin C. Yuan1,3, David L. Alderson2, Sean...Infected-Recovered (SIR) model. Based on these results, we determine the optimal alloca- tions of a limited quantity of vaccine between two non-interacting... vaccine , the deterministic model is a poor estimate of the optimal strategy for the more realistic, stochastic case. Introduction As rapid, long-range
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 ...
Network realization of triplet-type quantum stochastic systems
Zhou, Shaosheng; Fu, Shizhou; Chen, Yuping
2017-01-01
This paper focuses on a problem of network synthesis for a class of quantum stochastic systems. The systems under consideration are of triplet-type form and stem from linear quantum optics and linear quantum circuits. A new quantum network realization approach is proposed by generalizing the scattering operator from the scalar form to a unitary matrix in network components. It shows that the triplet-type quantum stochastic system can be approximated by a quantum network which consists of some one-degree-of-freedom generalized open-quantum harmonic oscillators (1DGQHOs) via series, concatenation and feedback connections.
Identification of linear stochastic systems through projection filters
Chen, Chung-Wen; Huang, Jen-Kuang; Juang, Jer-Nan
1992-01-01
A novel method is presented for identifying a state-space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relationship between the state-space model and the finite-difference model of linear stochastic systems derived through projection filters. It is proved that least-squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model.
Identification of Stochastic Wiener Systems using Indirect Inference
2015-01-01
We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is difficult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e.,~linear dynamic systems wi...
Average quantum dynamics of closed systems over stochastic Hamiltonians
Yu, Li
2011-01-01
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.
Estimating parameters in stochastic systems: A variational Bayesian approach
Vrettas, Michail D.; Cornford, Dan; Opper, Manfred
2011-11-01
This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.
Quality control system response to stochastic growth of amyloid fibrils
DEFF Research Database (Denmark)
Pigolotti, Simone; Lizana, Ludvig; Otzen, Daniel
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 t...
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 lar...
STABILITY CRITERIA FOR STOCHASTIC DISCRETE-TIME FRACTIONAL ORDER SYSTEMS
Directory of Open Access Journals (Sweden)
Carmen BARBACIORU
2016-05-01
Full Text Available In this paper are discussed stability problems for a class of discrete-time fractional systems (DTFSs with independent random perturbations. Two notions of mean square stability (MSS and mean square asymptotic stability (MSAS are introduced for the DTFSs by using an approximating linear stochastic system. Necessary and sufficient conditions for MSS and MSA are then derived.
An identification algorithm for linear stochastic systems with time delays
Leondes, C. T.; Wong, E. C.
1982-01-01
Linear discrete stochastic control systems containing unknown multiple time delays, plant parameters and noise variances are considered. An algorithm is established which uses the maximum-likelihood technique to identify the unknown parameters. An estimated likelihood function is evaluated based on the previous parameter estimates, which in turn generates a new descent direction vector to update the unknown parameters. The delays and plant parameters are identified in their respective parameter spaces. An example of a second-order stochastic system has been implemented by digital simulation to demonstrate the applicability of the algorithm.
? 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.
A higher-order numerical framework for stochastic simulation of chemical reaction systems.
Székely, Tamás; Burrage, Kevin; Erban, Radek; Zygalakis, Konstantinos C
2012-07-15
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. 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. 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.
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.
Feynman-Kac formula for stochastic hybrid systems
Bressloff, Paul C.
2017-01-01
We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.
Feynman-Kac formula for stochastic hybrid systems.
Bressloff, Paul C
2017-01-01
We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.
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...
A stochastic physical system approach to modeling river water quality
Curi, W. F.; Unny, T. E.; Kay, J. J.
1995-06-01
In this paper, concepts of network thermodynamics are applied to a river water quality model, which is based on Streeter-Phelps equations, to identify the corresponding physical components and their topology. Then, the randomness in the parameters, input coefficients and initial conditions are modeled by Gaussian white noises. From the stochastic components of the physical system description of problem and concepts of physical system theory, a set of stochastic differential equations can be automatically generated in a computer and the recent developments on the automatic formulation of the moment equations based on Ito calculus can be used. This procedure is illustrated through the solution of an example of stochastic river water quality problem and it is also shown how other related problems with different configurations can be automatically solved in a computer using just one software.
Compositional abstractions for long-run properties of stochastic systems
DEFF Research Database (Denmark)
Smith, Michael James Andrew
2011-01-01
When analysing the performance of a system, we are often interested in long-run properties, such as the proportion of time it spends in a certain state. Stochastic process algebras help us to answer this sort of question by building a compositional model of the system, and using tools to analyse...... its underlying Markov chain. However, this also leads to state space explosion problems as the number of components in the model increases, which severely limits the size of models we can analyse. Because of this, we look for abstraction techniques that allow us to analyse a smaller model that safely...... bounds the properties of the original. In this paper, we present an approach to bounding long-run properties of models in the stochastic process algebra PEPA. We use a method called stochastic bounds to build upper and lower bounds of the underlying Markov chain that are lumpable, and therefore can...
Identification and estimation algorithm for stochastic neural system.
Nakao, M; Hara, K; Kimura, M; Sato, R
1984-01-01
An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.
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.
Kierzek, Andrzej M; Zhou, Lu; Wanner, Barry L
2010-03-01
Two-component systems (TCSs) are prevalent signal transduction systems in bacteria that control innumerable adaptive responses to environmental cues and host-pathogen interactions. We constructed a detailed stochastic kinetic model of two component signalling based on published data. Our model has been validated with flow cytometry data and used to examine reporter gene expression in response to extracellular signal strength. The model shows that, depending on the actual kinetic parameters, TCSs exhibit all-or-none, graded or mixed mode responses. In accordance with other studies, positively autoregulated TCSs exhibit all-or-none responses. Unexpectedly, our model revealed that TCSs lacking a positive feedback loop exhibit not only graded but also mixed mode responses, in which variation of the signal strength alters the level of gene expression in induced cells while the regulated gene continues to be expressed at the basal level in a substantial fraction of cells. The graded response of the TCS changes to mixed mode response by an increase of the translation initiation rate of the histidine kinase. Thus, a TCS is an evolvable design pattern capable of implementing deterministic regulation and stochastic switches associated with both graded and threshold responses. This has implications for understanding the emergence of population diversity in pathogenic bacteria and the design of genetic circuits in synthetic biology applications. The model is available in systems biology markup language (SBML) and systems biology graphical notation (SBGN) formats and can be used as a component of large-scale biochemical reaction network models.
Theory and application of stability for stochastic reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
LUO Qi; DENG FeiQi; MAO XueRong; BAO JunDong; ZHANG YuTian
2008-01-01
So far, the Lyapunov direct method is still the moat effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding Ito formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the Ito stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, end exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob-tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.
Stochastic stage-structured modeling of the adaptive immune system
Energy Technology Data Exchange (ETDEWEB)
Chao, D. L. (Dennis L.); Davenport, M. P. (Miles P.); Forrest, S. (Stephanie); Perelson, Alan S.,
2003-01-01
We have constructed a computer model of the cytotoxic T lymphocyte (CTL) response to antigen and the maintenance of immunological memory. Because immune responses often begin with small numbers of cells and there is great variation among individual immune systems, we have chosen to implement a stochastic model that captures the life cycle of T cells more faithfully than deterministic models. Past models of the immune response have been differential equation based, which do not capture stochastic effects, or agent-based, which are computationally expensive. We use a stochastic stage-structured approach that has many of the advantages of agent-based modeling but is more efficient. Our model can provide insights into the effect infections have on the CTL repertoire and the response to subsequent infections.
Stochastic homogenization of rate-independent systems and applications
Heida, Martin
2017-05-01
We study the stochastic and periodic homogenization 1-homogeneous convex functionals. We prove some convergence results with respect to stochastic two-scale convergence, which are related to classical Γ -convergence results. The main result is a general \\liminf -estimate for a sequence of 1-homogeneous functionals and a two-scale stability result for sequences of convex sets. We apply our results to the homogenization of rate-independent systems with 1-homogeneous dissipation potentials and quadratic energies. In these applications, both the energy and the dissipation potential have an underlying stochastic microscopic structure. We study the particular homogenization problems of Prandtl-Reuss plasticity, Tresca friction on a macroscopic surface and Tresca friction on microscopic fissures.
Optimal adaptive control for a class of stochastic systems
Bagchi, Arunabha; Chen, Han-Fu
1997-01-01
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 w
Analysis of Stochastic Gilpin-Ayala Competition System
Directory of Open Access Journals (Sweden)
Lei Liu
2014-01-01
Full Text Available This paper is concerned with the asymptotic behavior for stochastic Gilpin-Ayala competition system. The sufficient conditions for existence of stationary distribution and extinction are established. And a certain asymptotic property of the solution is also obtained. A nontrivial example is provided to illustrate our results.
Parameter identification of stochastic diffusion systems with unknown boundary conditions
Aihara, Shin Ichi; Bagchi, Arunabha
2013-01-01
This paper treats the filtering and parameter identification for the stochastic diffusion systems with unknown boundary conditions. The physical situation of the unknown boundary conditions can be found in many industrial problems,i.g., the salt concentration model of the river Rhine is a typical ex
Prediction of the Stochastic System Properties Using Genetic Identification
2003-01-01
The article deals with the equation solutions for conditional probabilities determination. The number of variables in equation for correlation estimation could be reduced under the specific conditions. Stochastic system could be approximated by the mean values of the conditional probabilities as it declared by presented example.
Prediction of the Stochastic System Properties Using Genetic Identification
Directory of Open Access Journals (Sweden)
Juraj Spalek
2003-01-01
Full Text Available The article deals with the equation solutions for conditional probabilities determination. The number of variables in equation for correlation estimation could be reduced under the specific conditions. Stochastic system could be approximated by the mean values of the conditional probabilities as it declared by presented example.
Computational procedures for stochastic multi-echelon production systems
Houtum, van G.J.J.A.; Zijm, W.H.M.
1991-01-01
This paper is concerned with the numerical evaluation of multi-echelon production systems. Each stage requires a fixed predetermined leadtime; furthermore, we assume a stochastic, stationary end-time demand process. In a previous paper, we have developed an analytical framework for determining optim
Topics on the stochastical treatement of an open quantum system
Sturzu, I
2002-01-01
The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics, suggesting the definition of a Neumark-type dilation for the non-thermal states.
Stabilization of a Class of Stochastic Systems with Time Delays
Directory of Open Access Journals (Sweden)
Jian Wang
2014-01-01
Full Text Available The problem of exponential stability is investigated for a class of stochastic time-delay systems. By using the decomposition technique and Lyapunov stability theory, two improved exponential stability criteria are derived. Finally, a numerical example is given to illustrate the effectiveness and the benefit of the proposed method.
Experimental Analysis of Stochastic Resonance in a Duffing System
Institute of Scientific and Technical Information of China (English)
WANG Fu-Zhong; CHEN Wei-Shi; QIN Guang-Rong; GUO De-Yong; LIU Jun-Ling
2003-01-01
An experimental circuit is used to study the stochastic resonance (SR) phenomena in a Duffing system. The characteristics ofSR are investigated from various aspects by varying all the possible parameters. The deviations between the experimental results and the adiabatic theory are presented.
Analysis of Stochastic Gilpin-Ayala Competition System
Lei Liu; Quanxin Zhu
2014-01-01
This paper is concerned with the asymptotic behavior for stochastic Gilpin-Ayala competition system. The sufficient conditions for existence of stationary distribution and extinction are established. And a certain asymptotic property of the solution is also obtained. A nontrivial example is provided to illustrate our results.
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.
Time Evolution of the Dynamical Variables of a Stochastic System.
de la Pena, L.
1980-01-01
By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation-dissipation theorem to the time-dependent case. (Author/SK)
Simulating rare events in equilibrium or nonequilibrium stochastic systems
Allen, R.J.; Frenkel, D.; Wolde, P.R. ten
2006-01-01
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase-space density and are suitable for equilibrium or nonequilibrium systems in stationary state. A
Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
Blunt, N S; Kersten, J A F; Spencer, J S; Booth, George H; Alavi, Ali
2015-01-01
We expand upon the recent semi-stochastic adaptation to full configuration quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and demonstrate the resulting gains in stochastic efficiency for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the Beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.
Approximation of stochastic equilibria for dynamic systems with colored noise
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Ural Federal University, Lenina 51, Ekaterinburg, 620083 (Russian Federation)
2015-03-10
We consider nonlinear dynamic systems forced by colored noise. Using first approximation systems, we study dynamics of deviations of stochastic solutions from stable deterministic equilibria. Equations for the stationary second moments of deviations of random states are derived. An application of the elaborated theory to Van der Pol system driven by colored noise is given. A dependence of the dispersion on the time correlation of the colored noise is studied.
Statistical Study of Complex Eigenvalues in Stochastic Systems
Directory of Open Access Journals (Sweden)
Seifedine Kadry
2010-05-01
Full Text Available In this research we analyze the complex modes arising in multiple degree-of-freedom nonproportionally damped discrete linear stochastic systems. The complex eigenvalues intervene when unstable states like resonances, happened. Linear dynamic systems must generally be expected to exhibit non-proportional damping. Non-proportionally damped linear systems do not possess classical normal modes but possess complex modes. The proposed method is based on the transformation of random variables. The advantage of this method which give us the probability density function of real and imaginary part of the complex eigenvalue for stochastic mechanical system, i.e. a system with random output (Young's modulus, load. The proposed method is illustrated by considering numerical example based on a linear array of damped spring-mass oscillators. It is show n that the approach can predict the probability density function with good accuracy when compared with independent Monte-Carlo simulations.
TUNING OF GAUSSIAN STOCHASTIC-CONTROL SYSTEMS
VANSCHUPPEN, JH
1994-01-01
A closed-loop system consisting of a control system and an adaptive controller will be called tuning for a specified control objective if the real system and the ideal system defined below achieve the same value for the control objective. The real system is the system consisting of the unknown contr
Simulation of a class of delay stochastic system with distributed parameter
Institute of Scientific and Technical Information of China (English)
Song Yanan; Deng Feiqi; Luo Qi
2005-01-01
Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.
Description of interacting channel gating using a stochastic Markovian model.
Manivannan, K; Mathias, R T; Gudowska-Nowak, E
1996-01-01
Single-channel recordings from membrane patches frequently exhibit multiple conductance levels. In some preparations, the steady-state probabilities of observing these levels do not follow a binomial distribution. This behavior has been reported in sodium channels, potassium channels, acetylcholine receptor channels and gap junction channels. A non-binomial distribution suggests interaction of the channels or the presence of channels or the presence of channels with different open probabilities. However, the current trace sometimes exhibits single transitions spanning several levels. Since the probability of simultaneous transitions of independent channels is infinitesimally small, such observations strongly suggest a cooperative gating behavior. We present a Markov model to describe the cooperative gating of channels using only the all-points current amplitude histograms for the probability of observing the various conductance levels. We investigate the steady-state (or equilibrium) properties of a system of N channels and provide a scheme to express all the probabilities in terms of just two parameters. The main feature of our model is that lateral interaction of channels gives rise to cooperative gating. Another useful feature is the introduction of the language of graph theory which can potentially provide a different avenue to study ion channel kinetics. We write down explicit expressions for systems of two, three and four channels and provide a procedure to describe the system of N channels.
Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems
Directory of Open Access Journals (Sweden)
Ewelina Seroka
2015-01-01
Full Text Available The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.
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.
Stabilization of stochastic systems with hidden Markovian jumps
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper considers the adaptive control of discrete-time hybrid stochastic systems with unknown randomly jumping parameters described by a finite-state hidden Markov chain. An intuitive yet longstanding conjecture in this area is that such hybrid systems can be adaptively stabilized whenever the rate of transition of the hidden Markov chain is small enough. This paper provides a rigorous positive answer to this conjecture by establishing the global stability of a gradient-algorithm-based adaptive linear-quadratic control.
Current fluctuations in stochastic systems with long-range memory
Energy Technology Data Exchange (ETDEWEB)
Harris, R J; Touchette, H [School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom)], E-mail: rosemary.harris@qmul.ac.uk, E-mail: h.touchette@qmul.ac.uk
2009-08-28
We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti-Cohen fluctuation theorem. (fast track communication)
Stochastic transport of interacting particles in periodically driven ratchets
Savel'Ev, Sergey; Marchesoni, Fabio; Nori, Franco
2004-12-01
An open system of overdamped, interacting Brownian particles diffusing on a periodic substrate potential U(x+l)=U(x) is studied in terms of an infinite set of coupled partial differential equations describing the time evolution of the relevant many-particle distribution functions. In the mean-field approximation, this hierarchy of equations can be replaced by a nonlinear integro-differential Fokker-Planck equation. This is applicable when the distance a between particles is much less than the interaction length λ , i.e., a particle interacts with many others, resulting in averaging out fluctuations. The equation obtained in the mean-field approximation is applied to an ensemble of locally (a≪λ≪l) interacting (either repelling or attracting) particles placed in an asymmetric one-dimensional substrate potential, either with an oscillating temperature (temperature rachet) or driven by an ac force (rocked ratchet). In both cases we focus on the high-frequency limit. For the temperature ratchet, we find that the net current is typically suppressed (or can even be inverted) with increasing density of the repelling particles. In contrast, the net current through a rocked ratchet can be enhanced by increasing the density of the repelling particles. In the case of attracting particles, our perturbation technique is valid up to a critical value of the particle density, above which a finite fraction of the particles starts condensing in a liquidlike state near the substrate minima. The dependence of the net transport current on the particle density and the interparticle potential is analyzed in detail for different values of the ratchet parameters.
Fuzzy stochastic neural network model for structural system identification
Jiang, Xiaomo; Mahadevan, Sankaran; Yuan, Yong
2017-01-01
This paper presents a dynamic fuzzy stochastic neural network model for nonparametric system identification using ambient vibration data. The model is developed to handle two types of imprecision in the sensed data: fuzzy information and measurement uncertainties. The dimension of the input vector is determined by using the false nearest neighbor approach. A Bayesian information criterion is applied to obtain the optimum number of stochastic neurons in the model. A fuzzy C-means clustering algorithm is employed as a data mining tool to divide the sensed data into clusters with common features. The fuzzy stochastic model is created by combining the fuzzy clusters of input vectors with the radial basis activation functions in the stochastic neural network. A natural gradient method is developed based on the Kullback-Leibler distance criterion for quick convergence of the model training. The model is validated using a power density pseudospectrum approach and a Bayesian hypothesis testing-based metric. The proposed methodology is investigated with numerically simulated data from a Markov Chain model and a two-story planar frame, and experimentally sensed data from ambient vibration data of a benchmark structure.
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.
Energy Technology Data Exchange (ETDEWEB)
Laslett, L. Jackson.
1974-05-01
Detailed examination of computed particle trajectories has revealed a complexity and disorder that is of increasing interest to accelerator specialists. To introduce this topic, the author would like you to consider for a moment the analysis of synchrotron oscillations for a particle in a coasting beam, regarded as a problem in one degree of freedom. A simple analysis replaces the electric field of the RF-v cavity system by a traveling wave, having the speed of a synchronous reference particle, and leads to a pair of differential equations of the form dy/dn = -K sin {pi}x, (1A) where y measures the fractional departure of energy from the reference value {pi}x measures the electrical phase angle at which the particle traverses the cavity, and K is proportional to the cavity voltage; and dx/dn = {lambda}{prime}y, (1b) in which {lambda}{prime} is proportional to the change of revolution period with respect to particle energy. It will be recognized that these equations can be derived from a Hamiltonian function H = (1/2){lambda}{prime}y{sup 2}-(K/{pi})cos {pi}x. (2) Because this Hamiltonian function does not contain the independent variable explicitly, it will constitute a constant of the motion and possible trajectories in the x,y phase space will be just the curves defined by H = Constant, namely the familiar simple curves in phase space that are characteristic of a physical (non-linear) pendulum.
Pole assignment for stochastic systems with unknown coefficients
Institute of Scientific and Technical Information of China (English)
陈翰馥[1; 曹希仁[2
2000-01-01
This paper solves the exact pole assignment problem for the single-input stochastic systems with unknown coefficients under the controllability assumption which is necessary and sufficient for the arbitrary pole assignment for systems with known coefficients. The system noise is required to be mutually independent with zero mean and bounded second moment. Two approaches to solving the problem are proposed: One is the iterative learning approach which can be applied when the state at a fixed time can be repeatedly observed with different feedback gains; the other is the adaptive control approach which works when the trajectories satisfy a nondegeneracy condition. Both methods are essentially based on stochastic approximation, and the feedback gains are recursively given without invoking the certainty-equivalency-principle.
Processing in (linear) systems with stochastic input
Nutu, Catalin Silviu; Axinte, Tiberiu
2016-12-01
The paper is providing a different approach to real-world systems, such as micro and macro systems of our real life, where the man has little or no influence on the system, either not knowing the rules of the respective system or not knowing the input of the system, being thus mainly only spectator of the system's output. In such a system, the input of the system and the laws ruling the system could be only "guessed", based on intuition or previous knowledge of the analyzer of the respective system. But, as we will see in the paper, it exists also another, more theoretical and hence scientific way to approach the matter of the real-world systems, and this approach is mostly based on the theory related to Schrödinger's equation and the wave function associated with it and quantum mechanics as well. The main results of the paper are regarding the utilization of the Schrödinger's equation and related theory but also of the Quantum mechanics, in modeling real-life and real-world systems.
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
OPTIMUM DESIGN BASED ON RELIABILITY IN STOCHASTIC STRUCTURE SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The optimum design method based on the reliability is presented to the stochastic structure systems (i. e., the sectional area, length, elastic module and strength of the structural member are random variables) under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique(PNET) method were obtained. After derivation calculus, the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.
Dynamical entropy for systems with stochastic perturbation
Ostruszka, A; Slomczynski, W; Zyczkowski, K; Ostruszka, Andrzej; Pakonski, Prot; Slomczynski, Wojciech; Zyczkowski, Karol
1999-01-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is non negative and in the weak noise limit is conjectured to tend to the KS-entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel, for which the Frobenius-Perron operator can be represented by a finite matrix.
Dynamical entropy for systems with stochastic perturbation
Ostruszka; Pakonski; Slomczynski; Zyczkowski
2000-08-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyze the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is finite and non-negative and we call it the dynamical entropy of the noisy system. In the weak noise limit this quantity is conjectured to tend to the KS entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel for which the Frobenius-Perron operator can be represented by a finite matrix.
Stochastic image reconstruction for a dual-particle imaging system
Energy Technology Data Exchange (ETDEWEB)
Hamel, M.C., E-mail: mchamel@umich.edu [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States); Polack, J.K., E-mail: kpolack@umich.edu [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States); Poitrasson-Rivière, A., E-mail: alexispr@umich.edu [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States); Flaska, M., E-mail: mflaska@psu.edu [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States); Department of Mechanical and Nuclear Engineering, Pennsylvania State University, 137 Reber Building, University Park, PA 16802 (United States); Clarke, S.D., E-mail: clarkesd@umich.edu [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States); Pozzi, S.A., E-mail: pozzisa@umich.edu [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States); Tomanin, A., E-mail: alice.tomanin@jrc.ec.europa.eu [European Commission, Joint Research Centre, Institute for Transuranium Elements, 21027 Ispra, VA (Italy); Lainsa-Italia S.R.L., via E. Fermi 2749, 21027 Ispra, VA (Italy); Peerani, P., E-mail: paolo.peerani@jrc.ec.europa.eu [European Commission, Joint Research Centre, Institute for Transuranium Elements, 21027 Ispra, VA (Italy)
2016-02-21
Stochastic image reconstruction has been applied to a dual-particle imaging system being designed for nuclear safeguards applications. The dual-particle imager (DPI) is a combined Compton-scatter and neutron-scatter camera capable of producing separate neutron and photon images. The stochastic origin ensembles (SOE) method was investigated as an imaging method for the DPI because only a minimal estimation of system response is required to produce images with quality that is comparable to common maximum-likelihood methods. This work contains neutron and photon SOE image reconstructions for a {sup 252}Cf point source, two mixed-oxide (MOX) fuel canisters representing point sources, and the MOX fuel canisters representing a distributed source. Simulation of the DPI using MCNPX-PoliMi is validated by comparison of simulated and measured results. Because image quality is dependent on the number of counts and iterations used, the relationship between these quantities is investigated.
System Design Support by Optimization Method Using Stochastic Process
Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio
We proposed the new optimization method based on stochastic process. The characteristics of this method are to obtain the approximate solution of the optimum solution as an expected value. In numerical calculation, a kind of Monte Carlo method is used to obtain the solution because of stochastic process. Then, it can obtain the probability distribution of the design variable because it is generated in the probability that design variables were in proportion to the evaluation function value. This probability distribution shows the influence of design variables on the evaluation function value. This probability distribution is the information which is very useful for the system design. In this paper, it is shown the proposed method is useful for not only the optimization but also the system design. The flight trajectory optimization problem for the hang-glider is shown as an example of the numerical calculation.
Stochastic modelling of central heating systems
DEFF Research Database (Denmark)
Hansen, Lars Henrik
1997-01-01
and the degree Erhvervsforsker (a special Danish degree, equivalent to ``Industrial Ph.D.''). The thesis is mainly concerned with experimental design and system identification for individual components in water based central heating systems. The main contribution to this field is on the nonlinear dynamic...
System Identification using Measurements Subject to Stochastic Time Jitter
2004-01-01
When the sensors readings are perturbed by an unknown stochastic time jitter, classical system identification algorithms based on additive amplitude perturbations will give biased estimates. We here outline the maximum likelihood procedure, for the case of both time and amplitude noise, in the frequency domain, based on the measurement DFT. The method directly applies to output error continuous time models, while a simple sinusoid in noise example is used to illustrate the bias removal of the...
Digital set point control of nonlinear stochastic systems
Moose, R. L.; Vanlandingham, H. F.; Zwicke, P. E.
1978-01-01
A technique for digital control of nonlinear stochastic plants is presented. The development achieves a practical digital algorithm with which the closed-loop system behaves in a classical Type I manner even with gross nonlinearities in the plant structure and low signal-to-noise power ratios. The design procedure is explained in detail and illustrated by an example whose simulated responses testify to the practicality of the approach.
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.
STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS~
Institute of Scientific and Technical Information of China (English)
DengMaolin; HongMingchao; ZhuWeiqiu
2003-01-01
A strategy is proposed based on the stochastic averaging method for quasi nonintegrable Hamiltonian systems and the stochastic dynamical programming principle. The proposed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation. By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional averaged Ito stochastic differential equation. By using the stochastic dynamical programming principle the dynamical programming equation for minimizing the response of the system is formulated.The optimal control law is derived from the dynamical programming equation and the bounded control constraints. The response of optimally controlled systems is predicted through solving the FPK equation associated with It5 stochastic differential equation. An example is worked out in detail to illustrate the application of the control strategy proposed.
Accelerated Stochastic Simulation of Large Chemical Systems
Institute of Scientific and Technical Information of China (English)
CHEN Xiao; AO Ling
2007-01-01
For efficient simulation of chemical systems with large number of reactions, we report a fast and exact algorithm for direct simulation of chemical discrete Markov processes. The approach adopts the scheme of organizing the reactions into hierarchical groups. By generating a random number, the selection of the next reaction that actually occurs is accomplished by a few successive selections in the hierarchical groups. The algorithm which is suited for simulating systems with large number of reactions is much faster than the direct method or the optimized direct method. For a demonstration of its efficiency, the accelerated algorithm is applied to simulate the reaction-diffusion Brusselator model on a discretized space.
Stochastic self-monitoring of autonomous systems
2012-01-01
A probabilistic method is presented for high level task planning of autonomous, mobile systems under partial observability of states and partial knowledge of transition laws. Partial state observability is addressed by directed Markov fields which support the detection of relationships between pairs of observed variables in competition to other such pairs.
M Sakawa; Kato, K.
2009-01-01
This paper considers stochastic two-level linear programming problems. Using the concept of chance constraints and probability maximization, original problems are transformed into deterministic ones. An interactive fuzzy programming method is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance.
High Frequency Stochastic Resonance in Periodically Driven Systems
Dykman, M I
1993-01-01
Abstract: High frequency stochastic resonance (SR) phenomena, associated with fluctuational transitions between coexisting periodic attractors, have been investigated experimentally in an electronic model of a single-well Duffing oscillator bistable in a nearly resonant field of frequency $\\omega_F$. It is shown that, with increasing noise intensity, the signal/noise ratio (SNR) for a signal due to a weak trial force of frequency $\\Omega decreases again at higher noise intensities: behaviour similar to that observed previously for conventional (low frequency) SR in systems with static bistable potentials. The stochastic enhancement of the SNR of an additional signal at the mirror-reflected frequency $\\vert Ømega - 2 ømega_F \\vert$ is also observed, in accordance with theoretical predictions. Relationships with phenomena in nonlinear optics are discussed.
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
to evaluate year-to-year variation of wind power generation through a sensitivity analysis and to forecast very short-term wind power through a model-based prediction method. The stochastic load model is established on the basis of a seasonal autoregressive moving average (ARMA) process. It is demonstrated...... 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...... that minimizes the expectation of power losses of a 69-bus distribution system by controlling the power factor of WTs. The optimization is subjected to the probabilistic constraints of bus voltage and line current. The algorithm combines a constrained nonlinear optimization algorithm and a Monte Carlo based PLF...
Spontaneously stochastic solutions in one-dimensional inviscid systems
Mailybaev, Alexei A
2015-01-01
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a theoretical argument (with a detailed numerical confirmation) showing that a classical deterministic solution before a finite-time blowup, $t t_b$, representing a unique physically relevant description in the inviscid limit. This theory is based on the dynamical system formulation written for the logarithmic time $\\tau = \\log(t-t_b)$, which features a stable traveling wave solution for the inviscid Burgers equation, but a stochastic traveling wave for the Sabra model. The latter describes a universal onset of stochasticity immediately after the blowup.
Structured controllers for uncertain systems a stochastic optimization approach
Toscano, Rosario
2013-01-01
Structured Controllers for Uncertain Systems focuses on the development of easy-to-use design strategies for robust low-order or fixed-structure controllers (particularly the industrially ubiquitous PID controller). These strategies are based on a recently-developed stochastic optimization method termed the "Heuristic Kalman Algorithm" (HKA) the use of which results in a simplified methodology that enables the solution of the structured control problem without a profusion of user-defined parameters. An overview of the main stochastic methods employable in the context of continuous non-convex optimization problems is also provided and various optimization criteria for the design of a structured controller are considered; H∞, H2, and mixed H2/H∞ each merits a chapter to itself. Time-domain-performance specifications can be easily incorporated in the design. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technolo...
Spontaneously stochastic solutions in one-dimensional inviscid systems
Mailybaev, Alexei A.
2016-08-01
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a theoretical argument (with a detailed numerical confirmation) showing that a classical deterministic solution before a finite-time blowup, t t b , representing a unique physically relevant description in the inviscid limit. This theory is based on the dynamical system formulation written for the logarithmic time τ =log ≤ft(t-{{t}b}\\right) , which features a stable traveling wave solution for the inviscid Burgers equation, but a stochastic traveling wave for the Sabra model. The latter describes a universal onset of stochasticity immediately after the blowup.
The influence of stochastic dispersion on optical soliton system and its suppression
Institute of Scientific and Technical Information of China (English)
杨祥林; 温扬敬; 张明德
1995-01-01
The influence of stochastic dispersion on an optical soliton communication system is investigated, and the method of reducing this influence is also given. The analysis shows that the existence-of stochastic dispersion results in the arrival time jitter, which is in proportion to the mean square fluctuation of the imaginary component of stochastic dispersion and is related to soliton amplitude and velocity. The influence of stochastic dispersion can be reduced by using filtering method in frequency domain.
A Stochastic Calculus for Network Systems with Renewable Energy Sources
Wu, Kui; Marinakis, Dimitri
2011-01-01
We consider the performance modeling and evaluation of network systems powered with renewable energy sources such as solar and wind energy. Such energy sources largely depend on environmental conditions, which are hard to predict accurately. As such, it may only make sense to require the network systems to support a soft quality of service (QoS) guarantee, i.e., to guarantee a service requirement with a certain high probability. In this paper, we intend to build a solid mathematical foundation to help better understand the stochastic energy constraint and the inherent correlation between QoS and the uncertain energy supply. We utilize a calculus approach to model the cumulative amount of charged energy and the cumulative amount of consumed energy. We derive upper and lower bounds on the remaining energy level based on a stochastic energy charging rate and a stochastic energy discharging rate. By building the bridge between energy consumption and task execution (i.e., service), we study the QoS guarantee under...
Wang, Y. Y.; Huang, G. H.; Wang, S.; Li, W.; Guan, P. B.
2016-08-01
In this study, a risk-based interactive multi-stage stochastic programming (RIMSP) approach is proposed through incorporating the fractile criterion method and chance-constrained programming within a multi-stage decision-making framework. RIMSP is able to deal with dual uncertainties expressed as random boundary intervals that exist in the objective function and constraints. Moreover, RIMSP is capable of reflecting dynamics of uncertainties, as well as the trade-off between the total net benefit and the associated risk. A water allocation problem is used to illustrate applicability of the proposed methodology. A set of decision alternatives with different combinations of risk levels applied to the objective function and constraints can be generated for planning the water resources allocation system. The results can help decision makers examine potential interactions between risks related to the stochastic objective function and constraints. Furthermore, a number of solutions can be obtained under different water policy scenarios, which are useful for decision makers to formulate an appropriate policy under uncertainty. The performance of RIMSP is analyzed and compared with an inexact multi-stage stochastic programming (IMSP) method. Results of comparison experiment indicate that RIMSP is able to provide more robust water management alternatives with less system risks in comparison with IMSP.
Stochastic availability analysis of operational data systems in the Deep Space Network
Issa, T. N.
1991-01-01
Existing availability models of standby redundant systems consider only an operator's performance and its interaction with the hardware performance. In the case of operational data systems in the Deep Space Network (DSN), in addition to an operator system interface, a controller reconfigures the system and links a standby unit into the network data path upon failure of the operating unit. A stochastic (Markovian) process technique is used to model and analyze the availability performance and occurrence of degradation due to partial failures are quantitatively incorporated into the model. Exact expressions of the steady state availability and proportion degraded performance measures are derived for the systems under study. The interaction among the hardware, operator, and controller performance parameters and that interaction's effect on data availability are evaluated and illustrated for an operational data processing system.
Optimal policies for identification of stochastic linear systems
Lopez-Toledo, A. A.; Athans, M.
1975-01-01
The problem of designing closed-loop policies for identification of multiinput-multioutput linear discrete-time systems with random time-varying parameters is considered in this paper using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop laws. The computation of the optimal laws is shown to be nontrivial, an exercise in stochastic control, but open-loop, affine, and open-loop feedback optimal inputs are shown to yield tractable problems. Numerical examples are given. For time-invariant systems, the criterion considered is shown to be related to the trace of the information matrix associated with the system.
Distributed Fusion Receding Horizon Filtering in Linear Stochastic Systems
Directory of Open Access Journals (Sweden)
Il Young Song
2009-01-01
Full Text Available This paper presents a distributed receding horizon filtering algorithm for multisensor continuous-time linear stochastic systems. Distributed fusion with a weighted sum structure is applied to local receding horizon Kalman filters having different horizon lengths. The fusion estimate of the state of a dynamic system represents the optimal linear fusion by weighting matrices under the minimum mean square error criterion. The key contribution of this paper lies in the derivation of the differential equations for determining the error cross-covariances between the local receding horizon Kalman filters. The subsequent application of the proposed distributed filter to a linear dynamic system within a multisensor environment demonstrates its effectiveness.
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.
Bayesian inference for functional response in a stochastic predator-prey system.
Gilioli, Gianni; Pasquali, Sara; Ruggeri, Fabrizio
2008-02-01
We present a Bayesian method for functional response parameter estimation starting from time series of field data on predator-prey dynamics. Population dynamics is described by a system of stochastic differential equations in which behavioral stochasticities are represented by noise terms affecting each population as well as their interaction. We focus on the estimation of a behavioral parameter appearing in the functional response of predator to prey abundance when a small number of observations is available. To deal with small sample sizes, latent data are introduced between each pair of field observations and are considered as missing data. The method is applied to both simulated and observational data. The results obtained using different numbers of latent data are compared with those achieved following a frequentist approach. As a case study, we consider an acarine predator-prey system relevant to biological control problems.
Qian, Hong
2016-01-01
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity, but population wise with statistical rate laws in their syntheses, degradations, spatial diffusion, individual state transitions, and interactions. Such a formal kinetic system in a small volume $V$, like a single cell, can be rigorously treated in terms of a Markov process describing its nonlinear kinetics as well as nonequilibrium thermodynamics at a mesoscopic scale. We introduce notions such as open, driven chemical systems, entropy production, free energy dissipation, etc. Then in the macroscopic limit, we illustrate how two new "laws", in terms of a generalized free energy of the mesoscopic stochastic dynamics, emerge. Detailed balance and complex balance are two special classes of "simple" nonlinear kinetics. Phase transition is intrinsically related to multi-stability...
2015-01-01
National audience; In this paper, we focus on the stochastic block model (SBM),a probabilistic tool describing interactions between nodes of a network using latent clusters. The SBM assumes that the networkhas a stationary structure, in which connections of time varying intensity are not taken into account. In other words, interactions between two groups are forced to have the same features during the whole observation time. To overcome this limitation,we propose a partition of the whole time...
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.
Global parameter estimation methods for stochastic biochemical systems
Directory of Open Access Journals (Sweden)
Poovathingal Suresh
2010-08-01
Full Text Available Abstract Background The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data. Results Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality. Conclusions The parameter
Geng, Lingling; Yu, Yongguang; Zhang, Shuo
2016-09-01
In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.
The dynamical system of weathering: deterministic and stochastic analysis
Calabrese, S.; Parolari, A.; Porporato, A. M.
2016-12-01
The critical zone is fundamental to human society as it provides most of the ecosystem services such as food and fresh water. However, climate change and intense land use are threatening the critical zone, so that theoretical frameworks, to predict its future response, are needed. In this talk, a new modeling approach to evaluate the effect of hydrologic fluctuations on soil water chemistry and weathering reactions is analyzed by means of a dynamical system approach. In this model, equilibrium is assumed for the aqueous carbonate system while a kinetic law is adopted for the weathering reaction. Also, through an algebraic manipulation, we eliminate the equilibrium reactions and reduce the order of the system. We first analyze the deterministic temporal evolution, and study the stability of the nonlinear system and its trajectories, as a function of the hydro-climatic parameters. By introducing a stochastic rainfall forcing, we then analyze the system probabilistically, and through averaging techniques determine the inter-annual response of the nonlinear stochastic system to the climatic regime and hydrologic parameters (e.g., ET, soil texture). Some fundamental thermodynamic aspects of the chemical reactions are also discussed. By introducing the weathering reaction into the system, any mineral, such as calcium carbonate or a silicate mineral, can be considered.
Robust Fault Detection and Isolation for Stochastic Systems
George, Jemin; Gregory, Irene M.
2010-01-01
This paper outlines the formulation of a robust fault detection and isolation scheme that can precisely detect and isolate simultaneous actuator and sensor faults for uncertain linear stochastic systems. The given robust fault detection scheme based on the discontinuous robust observer approach would be able to distinguish between model uncertainties and actuator failures and therefore eliminate the problem of false alarms. Since the proposed approach involves precise reconstruction of sensor faults, it can also be used for sensor fault identification and the reconstruction of true outputs from faulty sensor outputs. Simulation results presented here validate the effectiveness of the robust fault detection and isolation system.
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
The stochastic separatrix and the reaction coordinate for complex systems.
Antoniou, Dimitri; Schwartz, Steven D
2009-04-21
We present a new approach to the identification of degrees of freedom which comprise a reaction coordinate in a complex system. The method begins with the generation of an ensemble of reactive trajectories. Each trajectory is analyzed for its equicommittor position or transition state; then the transition state ensemble is identified as the stochastic separatrix. Numerical analysis of the points along the separatrix for variability of coordinate location correctly identifies the components of the reaction coordinate in a test system of a double well coupled to a promoting vibration and a bath of linearly coupled oscillators.
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
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......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...
A Novel Stochastic Blind Adaptive Multiuser Detector for CDMA Systems
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Blind adaptive multiuser detector has become a research hotspot in recent years due to a number of advantages, but many blind adaptive algorithms involve low convergence rate. This paper presents a novel stochastic blind adaptive multiuser detector without requiring training sequences, which needs only two system parameters: the signature sequence of the desired user i, si and the variance of the additive white Gaussian noise (AWGN),σ2. Simulation results show that by reasonably choosing time varying step size, the proposed detector can not only improve the convergence rate, but also reduce the limiting NSE (Normalized Squared Error) values, so it can effectively increase the performance of the system.
Nonlinear stochastic system identification of skin using volterra kernels.
Chen, Yi; Hunter, Ian W
2013-04-01
Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy.
Dynamical simulations of classical stochastic systems using matrix product states.
Johnson, T H; Clark, S R; Jaksch, D
2010-09-01
We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of one-dimensional quantum systems, to simulate the time evolution of nonequilibrium stochastic systems. We describe this method in detail; a system's probability distribution is represented by a matrix product state (MPS) of finite dimension and then its time evolution is efficiently simulated by repeatedly updating and approximately refactorizing this representation. We examine the use of MPS as an approximation method, looking at parallels between the interpretations of applying it to quantum state vectors and probability distributions. In the context of stochastic systems we consider two types of factorization for use in the TEBD algorithm: non-negative matrix factorization (NMF), which ensures that the approximate probability distribution is manifestly non-negative, and the singular value decomposition (SVD). Comparing these factorizations, we find the accuracy of the SVD to be substantially greater than current NMF algorithms. We then apply TEBD to simulate the totally asymmetric simple exclusion process (TASEP) for systems of up to hundreds of lattice sites in size. Using exact analytic results for the TASEP steady state, we find that TEBD reproduces this state such that the error in calculating expectation values can be made negligible even when severely compressing the description of the system by restricting the dimension of the MPS to be very small. Out of the steady state we show for specific observables that expectation values converge as the dimension of the MPS is increased to a moderate size.
Stochastic P systems and the simulation of biochemical processes with dynamic compartments.
Spicher, Antoine; Michel, Olivier; Cieslak, Mikolaj; Giavitto, Jean-Louis; Prusinkiewicz, Przemyslaw
2008-03-01
We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.
Chavanis, P. H.; Delfini, L.
2014-03-01
We study random transitions between two metastable states that appear below a critical temperature in a one-dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a homogeneous phase to an inhomogeneous phase [P. H. Chavanis and L. Delfini, Phys. Rev. E 81, 051103 (2010), 10.1103/PhysRevE.81.051103]. We numerically solve the N-body Langevin equations and the stochastic Smoluchowski-Poisson system, which takes fluctuations (finite N effects) into account. The system switches back and forth between the two metastable states (bistability) and the particles accumulate successively at the center or at the boundary of the domain. We explicitly show that these random transitions exhibit the phenomenology of the ordinary Kramers problem for a Brownian particle in a double-well potential. The distribution of the residence time is Poissonian and the average lifetime of a metastable state is given by the Arrhenius law; i.e., it is proportional to the exponential of the barrier of free energy ΔF divided by the energy of thermal excitation kBT. Since the free energy is proportional to the number of particles N for a system with long-range interactions, the lifetime of metastable states scales as eN and is considerable for N ≫1. As a result, in many applications, metastable states of systems with long-range interactions can be considered as stable states. However, for moderate values of N, or close to a critical point, the lifetime of the metastable states is reduced since the barrier of free energy decreases. In that case, the fluctuations become important and the mean field approximation is no more valid. This is the situation considered in this paper. By an appropriate change of notations, our results also apply to bacterial populations experiencing chemotaxis in biology. Their dynamics can be described by a stochastic Keller-Segel model that takes fluctuations into account and goes beyond the usual mean
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.
Stochastic switching in slow-fast systems: a large-fluctuation approach.
Heckman, Christoffer R; Schwartz, Ira B
2014-02-01
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we model rare event occurrences due to large fluctuations probabilistically and employ a WKB ansatz to approximate their rate of occurrence. This results in the generation of a two-point boundary value problem that models the interaction of the state variables and the most likely noise force required to induce a rare event. The resulting equations of motion of describing the phenomenon are shown to be singularly perturbed. Vastly different time scales among the variables are leveraged to reduce the dimension and predict the dynamics on the slow manifold in a deterministic setting. The resulting constrained equations of motion may be used to directly compute an exponent that determines the probability of rare events. To verify the theory, a stochastic damped Duffing oscillator with three equilibrium points (two sinks separated by a saddle) is analyzed. The predicted switching time between states is computed using the optimal path that resides in an expanded phase space. We show that the exponential scaling of the switching rate as a function of system parameters agrees well with numerical simulations. Moreover, the dynamics of the original system and the reduced system via center manifolds are shown to agree in an exponentially scaling sense.
Earthquake nucleation in a stochastic fault model of globally coupled units with interaction delays
Vasović, Nebojša; Kostić, Srđan; Franović, Igor; Todorović, Kristina
2016-09-01
In present paper we analyze dynamics of fault motion by considering delayed interaction of 100 all-to-all coupled blocks with rate-dependent friction law in presence of random seismic noise. Such a model sufficiently well describes a real fault motion, whose prevailing stochastic nature is implied by surrogate data analysis of available GPS measurements of active fault movement. Interaction of blocks in an analyzed model is studied as a function of time delay, observed both for dynamics of individual faults and phenomenological models. Analyzed model is examined as a system of all-to-all coupled blocks according to typical assumption of compound faults as complex of globally coupled segments. We apply numerical methods to show that there are local bifurcations from equilibrium state to periodic oscillations, with an occurrence of irregular aperiodic behavior when initial conditions are set away from the equilibrium point. Such a behavior indicates a possible existence of a bi-stable dynamical regime, due to effect of the introduced seismic noise or the existence of global attractor. The latter assumption is additionally confirmed by analyzing the corresponding mean-field approximated model. In this bi-stable regime, distribution of event magnitudes follows Gutenberg-Richter power law with satisfying statistical accuracy, including the b-value within the real observed range.
Discrete Time Optimal Adaptive Control for Linear Stochastic Systems
Institute of Scientific and Technical Information of China (English)
JIANG Rui; LUO Guiming
2007-01-01
The least-squares(LS)algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares(WLS)algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for daptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller,this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.
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
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......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...... 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...
Institute of Scientific and Technical Information of China (English)
Yongjun Wu; Wang Fang
2008-01-01
The first-passage statistics of Duffing-Rayleigh-Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the correspon-ding backward Kolmogorov equation and Pontryagin equa-tion are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.
Towards sub-optimal stochastic control of partially observable stochastic systems
Ruzicka, G. J.
1980-01-01
The paper deals with a class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in n dimensions is proved.
H {sub {infinity}} analysis of nonlinear stochastic time-delay systems
Energy Technology Data Exchange (ETDEWEB)
Shu Huisheng [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)] e-mail: hsshu@dhu.edu.cn; Wei Guoliang [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)
2005-10-01
In this paper, the H {sub {infinity}} analysis problem is studied for a general class of nonlinear stochastic systems with time-delay. The stochastic systems are described in terms of stochastic functional differential equations. The Razumikhin-type lemma is employed to establish sufficient conditions for the time-delay stochastic systems to be internally stable, and the H {sub {infinity}} analysis problem is studied in order to quantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system. In particular, the paper obtains the general conditions under which the L {sub 2} gain of the system is less than or equal to a given constant. Some easy-to-test criteria are also given so as to determine whether the nonlinear stochastic time-delay system under investigation is internally stable and whether it achieves certain H {sub {infinity}} performance index. Finally, illustrative examples are provided to show the usefulness of the proposed theory.
Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.
Stochastic systems driven by alpha-stable noises
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Ditlevsen, P.
1998-01-01
It has almost become a standard in stochastic mechanics applications of stochasticdifferential equations that the driving forces are modeled as Gaussian white noises, that is, as scalar or vector Brownianmotion increments.However, this modeling may not always lead to responses that comply well...... with observed data. In particular the tailsof the observed response distributions may even for linear systems be more fat than the tails obtained for Gaussianwhite noise input. Also the excitation may show jumps that cannot be modeled by Gaussian white noise. The paper supports the possibility of using...
Stochastic modeling of unresolved scales in complex systems
Institute of Scientific and Technical Information of China (English)
Jinqiao DUAN
2009-01-01
Model uncertainties or simulation uncertainties occur in math-ematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., 'unresolved') due to a lack in our understand-ing of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy.
Stochastic Lattice Gas Model for a Predator-Prey System
Satulovsky, J E; Satulovsky, Javier; Tome, Tania
1994-01-01
We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by using a dynamical mean-field approximation and computer simulations. Our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators. For the sets of parameters used in our computer simulations, these oscillations occur at a local level. Mean-field results predict synchronized collective oscillations.
Stochastic Analysis and Design of Heterogeneous Microstructural Materials System
Xu, Hongyi
Advanced materials system refers to new materials that are comprised of multiple traditional constituents but complex microstructure morphologies, which lead to superior properties over the conventional materials. To accelerate the development of new advanced materials system, the objective of this dissertation is to develop a computational design framework and the associated techniques for design automation of microstructure materials systems, with an emphasis on addressing the uncertainties associated with the heterogeneity of microstructural materials. Five key research tasks are identified: design representation, design evaluation, design synthesis, material informatics and uncertainty quantification. Design representation of microstructure includes statistical characterization and stochastic reconstruction. This dissertation develops a new descriptor-based methodology, which characterizes 2D microstructures using descriptors of composition, dispersion and geometry. Statistics of 3D descriptors are predicted based on 2D information to enable 2D-to-3D reconstruction. An efficient sequential reconstruction algorithm is developed to reconstruct statistically equivalent random 3D digital microstructures. In design evaluation, a stochastic decomposition and reassembly strategy is developed to deal with the high computational costs and uncertainties induced by material heterogeneity. The properties of Representative Volume Elements (RVE) are predicted by stochastically reassembling SVE elements with stochastic properties into a coarse representation of the RVE. In design synthesis, a new descriptor-based design framework is developed, which integrates computational methods of microstructure characterization and reconstruction, sensitivity analysis, Design of Experiments (DOE), metamodeling and optimization the enable parametric optimization of the microstructure for achieving the desired material properties. Material informatics is studied to efficiently reduce the
EXISTENCE AND UNIQUENESS AND STABILITY OF SOLUTIONS FOR STOCHASTIC IMPULSIVE SYSTEMS
Institute of Scientific and Technical Information of China (English)
Bin LIU; Xinzhi LIU; Xiaoxin LIAO
2007-01-01
This paper studies the existence,uniqueness,and stability of solutions for stochastic impul sive systems.By employing Lyapunov-like functions,some sufficient conditions of the global existence,uniqueness,and stability of solutions for stochastic impulsive systems are established.Furthermore,the results are specialized to the case of linear stochastic impulsive systems.Finally,some examples are given to illustrate the applications of our theory.
Controllability of nonlinear stochastic systems with multiple time-varying delays in control
Directory of Open Access Journals (Sweden)
Karthikeyan Shanmugasundaram
2015-06-01
Full Text Available This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.
Fluctuations as stochastic deformation
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
McKetterick, Thomas John; Giuggioli, Luca
2014-10-01
Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.
Abramov, Rafail V.
2017-03-01
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes.
Stochastic model of agent interaction with opinion leaders
Ellero, Andrea; Fasano, Giovanni; Sorato, Annamaria
2013-04-01
We analyze the problem of agents' interactions in a given population. The purpose of this paper is twofold. Starting from a scheme proposed by Galam [Physica A0378-437110.1016/S0378-4371(02)01582-0 320, 571 (2003)], which is based on a majority rule to treat the individuals’ interactions, we first study some of its relevant properties. Then, we introduce special individuals, called opinion leaders, who play a key role in information spreading in several practical applications. Opinion leaders have the special feature of strongly interfering with the process based on the majority rule, speeding up the diffusion. We consider a model describing agents’ interactions, which encompasses Galam's proposal, where opinion leaders are included as special agents. Then we study its specific properties which significantly recast and extend some conclusions drawn for the models given by Galam and Ellero, Fasano, and Sorato [Physica A0378-437110.1016/j.physa.2009.06.002 388, 3901 (2009)]. Finally, we provide theoretical and numerical results concerning the dynamics of our model, showing that a small percentage of opinion leaders may both accelerate and/or even reverse the overall consensus among all the agents.
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
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
games that does not require finding solutions to nonlinear partial differential equations or solv- ing backward stochastic differential equations ...for stochastic partial differential equations with fractional Brownian motions having the Hurst parameter in the interval (1/2,1), which includes the...Linear exponential-quadratic control problems for stochastic partial differential equations are explicitly solved. Discrete time linear quadratic
A Stochastic Decision Support System for Economic Order Quantity Problem
Directory of Open Access Journals (Sweden)
Amir Yousefli
2012-01-01
Full Text Available Improving decisions efficiency is one of the major concerns of the decision support systems. Specially in the uncertain environment, decision support systems could be implemented efficiently to simplify decision making process. In this paper stochastic economic order quantity (EOQ problem is investigated in which decision variables and objective function are uncertain in nature and optimum probability distribution functions of them are calculated through a geometric programming model. Obtained probability distribution functions of the decision variables and the objective function are used as optimum knowledge to design a new probabilistic rule base (PRB as a decision support system for EOQ model. The developed PRB is a new type of the stochastic rule bases that can be used to infer optimum or near optimum values of the decision variables and the objective function of the EOQ model without solving the geometric programming problem directly. Comparison between the results of the developed PRB and the optimum solutions which is provided in the numerical example illustrates the efficiency of the developed PRB.
Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps.
Srokowski, Tomasz
2015-05-01
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general Lévy stable statistics and experiences long rests due to nonhomogeneously distributed traps. The memory is taken into account by subordination of that process to a random time; then the subordination equation is position dependent. The problem is approximated by a decoupling of the medium structure and memory and exactly solved for a power-law position dependence of the memory. In the case of the Gaussian statistics, the density distribution and moments are derived: depending on geometry and memory parameters, the system may reveal both the subdiffusion and enhanced diffusion. The similar analysis is performed for the Lévy flights where the finiteness of the variance follows from a variable noise intensity near a boundary. Two diffusion regimes are found: in the bulk and near the surface. The anomalous diffusion exponent as a function of the system parameters is derived.
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.
Energy Technology Data Exchange (ETDEWEB)
Hsiang, J.-T., E-mail: cosmology@gmail.com [Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433 (China); Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan (China); Hu, B.L. [Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433 (China); Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742 (United States)
2015-11-15
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
Indirect Identification of Linear Stochastic Systems with Known Feedback Dynamics
Huang, Jen-Kuang; Hsiao, Min-Hung; Cox, David E.
1996-01-01
An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.
Robust Performance And Dissipation of Stochastic Control Systems
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro
The topic of the present dissertation is robustness and performance issues in nonlinear control systems. The control systems in our study are described by nominal models consisting of nonlinear deterministic or stochastic differential equations in a Euclidean state space. The nominal models...... and topology on the space of supply rates. For instance, we give conditions under which the available storage is a continuous convex function of the supply rate. Dissipation theory in the existing literature applies only to deterministic systems. This is unfortunate since robust control applications typically...... are subject to perturbations which are completely unknown dynamic systems, except that they are known to possess certain properties of dissipation. A dissipation property restricts the dynamic behaviour of the perturbation to conform with a bounded resource; for instance energy. The main contribution...
Stochastic Background of Gravitational Waves Generated by Compact Binary Systems
Evangelista, E F D
2015-01-01
Binary Systems are the most studied sources of gravitational waves. The mechanisms of emission and the behavior of the orbital parameters are well known and can be written in analytic form in several cases. Besides, the strongest indication of the existence of gravitational waves has arisen from the observation of binary systems. On the other hand, when the detection of gravitational radiation becomes a reality, one of the observed pattern of the signals will be probably of stochastic background nature, which are characterized by a superposition of signals emitted by many sources around the universe. Our aim here is to develop an alternative method of calculating such backgrounds emitted by cosmological compact binary systems during their periodic or quasiperiodic phases. We use an analogy with a problem of Statistical Mechanics in order to perform this sum as well as taking into account the temporal variation of the orbital parameters of the systems. Such a kind of background is of particular importance sinc...
Hsu, Chieh; Scherrer, Simone; Buetti-Dinh, Antoine; Ratna, Prasuna; Pizzolato, Julia; Jaquet, Vincent; Becskei, Attila
2012-01-01
During evolution, genetic networks are rewired through strengthening or weakening their interactions to develop new regulatory schemes. In the galactose network, the GAL1/GAL3 paralogues and the GAL2 gene enhance their own expression mediated by the Gal4p transcriptional activator. The wiring strength in these feedback loops is set by the number of Gal4p binding sites. Here we show using synthetic circuits that multiplying the binding sites increases the expression of a gene under the direct control of an activator, but this enhancement is not fed back in the circuit. The feedback loops are rather activated by genes that have frequent stochastic bursts and fast RNA decay rates. In this way, rapid adaptation to galactose can be triggered even by weakly expressed genes. Our results indicate that nonlinear stochastic transcriptional responses enable feedback loops to function autonomously, or contrary to what is dictated by the strength of interactions enclosing the circuit. PMID:22353713
On features of magnetization self-organization in 1D stochastic ferromagnetic systems
Ivanov, Anatoly A.; Orlov, Vitaly A.
2017-03-01
The magnetic structure of a polycrystalline nanowire at the weak or missing magnetostatic interaction exhibits the special self-organization of magnetization. As is known, the magnetization structure forming in a random crystallographic anisotropy field has a characteristic length range, which involves tens and hundreds of crystallites. This leads to the occurrence of stochastic domains. The induced uniform anisotropy of magnetostatic nature or the texture co-directed with the crystallite anisotropy axes masks the picture of stochastic domains. Nevertheless, as we show, the information on stochastic domains remains in the magnetization structure. The experimental techniques for obtaining information on the magnetic properties of stochastic domains are proposed.
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.
A stochastic perturbation theory for non-autonomous systems
Moon, Woosok; Wettlaufer, John
2014-05-01
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 ΔF0. The deterministic model, developed by Eisenman and Wettlaufer EW09 exhibits several transitions as ΔF0 increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system. Eisenman, I., and J. S. Wettlaufer, 'Nonlinear threshold behavior during the loss of Arctic sea ice,' Proc. Natl. Acad. Sci. USA, 106, 28-32, 2009.
Stochastic response of nonlinear system in probability domain
Indian Academy of Sciences (India)
Deepak Kumar; T K Datta
2006-08-01
A stochastic averaging procedure for obtaining the probability density function (PDF) of the response for a strongly nonlinear single-degree-of-freedom system, subjected to both multiplicative and additive random excitations is presented. The procedure uses random Van Der Pol transformation, Ito’s equation of limiting diffusion process and stochastic averaging technique as outlined by Zhu and others. However, the equations are rederived in generalized form and arranged in such a way that the procedure lends itself to a numerical computational scheme using FFT. The main objective of the modiﬁcation is to consider highly irregular nonlinear functions which cannot be integrated in closed form and also to solve problems where analytical expressions for probability density function cannot be obtained. The procedure is applied to obtain the PDF of the response of Dufﬁng oscillator subjected to additive and multiplicative random excitations represented by rational power spectral density functions (PSDFs). The results are veriﬁed by digital simulation. It is shown that the procedure provides results which compare very well with those obtained from simulation analysis not only for wide-band excitations but also for very narrow-band excitations, which are weak (when normalized with respect to mass of the system).
Dynamic Interactive Learning Systems
Sabry, Khaled; Barker, Jeff
2009-01-01
This paper reviews and discusses the notions of interactivity and dynamicity of learning systems in relation to information technologies and design principles that can contribute to interactive and dynamic learning. It explores the concept of dynamic interactive learning systems based on the emerging generation of information as part of a…
Driven random-phase three-wave interactions: Cycles, bursts, and stochasticity
Energy Technology Data Exchange (ETDEWEB)
Robinson, P.A. (School of Physics, University of Sydney, NSW 2006 (Australia))
1992-11-01
Steadily driven, undriven, and stochastically driven three-wave decay processes involving groups of random-phase waves are investigated analytically and numerically. Steadily driven systems in which one product wave is suppressed exhibit neutrally stable Lotka--Volterra cycles, as for the true two-component case, whereas three-component systems are stable below a critical driver strength and unstable beyond that point. Initially unstable, but undriven, systems produce bursts of product waves, after which the parent waves fall to a final level that is an exponentially decreasing function of their initial level. Three-component systems where the product waves have near-equal dissipation rates are an exception to the latter behavior; in such systems the final parent-wave level is almost independent of the initial one. Stochastic driving gives rise to bursts of product waves in a cycle of fluctuating period, whereas a low-level noise source tends to stabilize the system.
Yang, Yongge; Xu, Wei; Sun, Yahui; Xiao, Yanwen
2017-01-01
This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.
Directory of Open Access Journals (Sweden)
Jiang Wu
2016-01-01
Full Text Available This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.
Progress of the stochastic cooling system of the Collector Ring
Dimopoulou, C; Bohm, R; Dolinskyy, O; Franzke, B; Hettrich, R; Maier, W; Menges, R; Nolden, F; Peschke, C; Petri, P; Steck, M; Thorndahl, L
2013-01-01
An overview of the recent achievements and ongoing developments for the stochastic cooling system of the Collector Ring is given. In focus are the hardware developments as well as the progress in predicting the system performance. The system operates in the frequency band 1-2 GHz, it has to provide fast 3D cooling of antiproton, rare isotope and stable heavy ion beams. The main challenges are (i) the cooling of antiprotons by means of cryogenic movable pick-up electrodes and (ii) the fast two-stage cooling (pre-cooling by the Palmer method, followed by the notch filter method) of the hot rare isotope beams (RIBs). Recently, a novel code for simulating the cooling process in the time domain has been developed at CERN. First results for the momentum cooling for heavy ions in the CR will be shown in comparison with results obtained in the frequency domain with the Fokker-Planck approach.
Stochastic Shadowing and Stochastic Stability
Todorov, Dmitry
2014-01-01
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.
Modified stochastic variational approach to non-Hermitian quantum systems
Kraft, Daniel; Plessas, Willibald
2016-08-01
The stochastic variational method has proven to be a very efficient and accurate tool to calculate especially bound states of quantum-mechanical few-body systems. It relies on the Rayleigh-Ritz variational principle for minimizing real eigenenergies of Hermitian Hamiltonians. From molecular to atomic, nuclear, and particle physics there is actually a great demand of describing also resonant states to a high degree of reliance. This is especially true with regard to hadron resonances, which have to be treated in a relativistic framework. So far standard methods of dealing with quantum chromodynamics have not yet succeeded in describing hadron resonances in a realistic manner. Resonant states can be handled by non-Hermitian quantum Hamiltonians. These states correspond to poles in the lower half of the unphysical sheet of the complex energy plane and are therefore intimately connected with complex eigenvalues. Consequently the Rayleigh-Ritz variational principle cannot be employed in the usual manner. We have studied alternative selection principles for the choice of test functions to treat resonances along the stochastic variational method. We have found that a stationarity principle for the complex energy eigenvalues provides a viable method for selecting test functions for resonant states in a constructive manner. We discuss several variants thereof and exemplify their practical efficiencies.
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...
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.
Parameter identification of linear discrete stochastic systems with time delays
Wong, E. C.
1980-01-01
An identification algorithm that uses the maximum likelihood technique to identify the unknown time delays, plant parameters, and noise covariances of linear discrete stochastic systems is presented. Cases of additive white noise and colored measurement noises are considered. The likelihood function is evaluated using either a minimum-variance (Kalman) filter or a minimal-order observer. The Kalman filter is used in the identification algorithm to provide minimum-variance estimates. The minimal-order observer is a lower-dimensional and computationally simpler filter, and is advantageous especially for systems with long delays. It provides a less optimal solution to the minimum-mean-square state estimation problem. The colored-noise observer algorithm has the disadvantage of having to compute an extra error covariance matrix of lower order.
Adaptive robust control of nonholonomic systems with stochastic disturbances
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances. The objective is to design the almost global adaptive asymptotical controllers in probability u0 and u1 for the systems by using discontinuous control. A switching control law u0 is designed to almost globally asymptotically stabilize the state x0 in both the singular x0 (t0)=0 case and the non-singular x0 (t0)≠0 case. Then the state scaling technique is introduced for the discontinuous feedback into the (x1, x2, …, xn)-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law u1 has been presented for (x1, x2, …, xn) -subsystem for both different u0 in non-singular x0 (t0)≠0 case and the singular case x0 (t0)=0. The control algorithm validity is proved by simulation.
Study of the nonlinear longitudinal dynamics of a stochastic system
Directory of Open Access Journals (Sweden)
Cunha Americo
2014-01-01
Full Text Available This paper deals with the theoretical study of how discrete elements attached to a continuous stochastic systems can affect their dynamical behavior. For this, it is studied the nonlinear longitudinal dynamics of an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. Numerical simulations are conducted and their results are analyzed in function of the ratio between the masses of the discrete and the continuous parts of the system. This analysis reveals that the dynamic behavior of the bar is significantly altered when the lumped mass is varied, being more inﬂuenced by the randomness for small values of the lumped mass.
Online prediction and control in nonlinear stochastic systems
DEFF Research Database (Denmark)
Nielsen, Torben Skov
2002-01-01
of systems which are inherently non-stationary. The third part concerns the issue of predicting the power production from wind turbines in the presence of Numerical Weather Predictions (NWP) of selected climatical variables. Here the transformation through the wind turbines from (primarily) wind speed....... The papers G , H and J investigate models and methods for predicting wind power from a wind farm on basis of observations and numerical weather predictions. All three papers consider multistep prediction models, but uses di erent estimation methods as well as dierent models for the diurnal variation of wind......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...
Institute of Scientific and Technical Information of China (English)
Jiang Zhibin; He Junming
2003-01-01
Object-oriented Petri nets (OPNs) is extended into stochastic object-oriented Petri nets (SOPNs) by associating the OPN of an object with stochastic transitions and introducing stochastic places. The stochastic transition of the SOPNs of a production resources can be used to model its reliability, while the SOPN of a production resource can describe its performance with reliability considered. The SOPN model of a case production system is built to illustrate the relationship between the system's performances and the failures of individual production resources.
Frank, T D
2002-07-01
Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.
Frequency modulation of stochastic gene expression bursts by strongly interacting small RNAs
Kumar, Niraj; Jia, Tao; Zarringhalam, Kourosh; Kulkarni, Rahul V.
2016-10-01
The sporadic nature of gene expression at the single-cell level—long periods of inactivity punctuated by bursts of mRNA or protein production—plays a critical role in diverse cellular processes. To elucidate the cellular role of bursting in gene expression, synthetic biology approaches have been used to design simple genetic circuits with bursty mRNA or protein production. Understanding how such genetic circuits can be designed with the ability to control burst-related parameters requires the development of quantitative stochastic models of gene expression. In this work, we analyze stochastic models for the regulation of gene expression bursts by strongly interacting small RNAs. For the parameter range considered, results based on mean-field approaches are significantly inaccurate and alternative analytical approaches are needed. Using simplifying approximations, we obtain analytical results for the corresponding steady-state distributions that are in agreement with results from stochastic simulations. These results indicate that regulation by small RNAs, in the strong interaction limit, can be used to effectively modulate the frequency of bursting. We explore the consequences of such regulation for simple genetic circuits involving feedback effects and switching between promoter states.
Frequency modulation of stochastic gene expression bursts by strongly interacting small RNAs.
Kumar, Niraj; Jia, Tao; Zarringhalam, Kourosh; Kulkarni, Rahul V
2016-10-01
The sporadic nature of gene expression at the single-cell level-long periods of inactivity punctuated by bursts of mRNA or protein production-plays a critical role in diverse cellular processes. To elucidate the cellular role of bursting in gene expression, synthetic biology approaches have been used to design simple genetic circuits with bursty mRNA or protein production. Understanding how such genetic circuits can be designed with the ability to control burst-related parameters requires the development of quantitative stochastic models of gene expression. In this work, we analyze stochastic models for the regulation of gene expression bursts by strongly interacting small RNAs. For the parameter range considered, results based on mean-field approaches are significantly inaccurate and alternative analytical approaches are needed. Using simplifying approximations, we obtain analytical results for the corresponding steady-state distributions that are in agreement with results from stochastic simulations. These results indicate that regulation by small RNAs, in the strong interaction limit, can be used to effectively modulate the frequency of bursting. We explore the consequences of such regulation for simple genetic circuits involving feedback effects and switching between promoter states.
Stochastic State Space Modelling of Nonlinear systems - With application to Marine Ecosystems
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg
to conflict with the concept of mass balances. One of the central conclusions of the thesis is that the stochastic formulations should be an integral part of the model formulation. As discrete-time stochastic processes are simpler to handle numerically than continuous-time stochastic processes, I start......This thesis deals with stochastic dynamical systems in discrete and continuous time. Traditionally dynamical systems in continuous time are modelled using Ordinary Differential Equations (ODEs). Even the most complex system of ODEs will not be able to capture every detail of a complex system like...... a natural ecosystem, and hence residual variation between the model and observations will always remain. In stochastic state-space models the residual variation is separated into observation and system noise and a main theme of the thesis is a proper description of the system noise. Additive Gaussian noise...
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
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...
Classical Solutions of Path-Dependent PDEs and Functional Forward-Backward Stochastic Systems
Directory of Open Access Journals (Sweden)
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.
H∞ Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise
Directory of Open Access Journals (Sweden)
Ming Gao
2015-01-01
Full Text Available This paper studies the infinite horizon H∞ control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean square H∞ control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.
Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation
Institute of Scientific and Technical Information of China (English)
Rong-hua HUAN; Wei-qiu ZHU; Yong-jun WU
2008-01-01
A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged It6 stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged It6 equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.
Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity
Florchinger, Patrick
2016-07-01
The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.
Setting development goals using stochastic dynamical system models
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. PMID:28241057
Nonequilibrium Steady States of a Stochastic Model System.
Zhang, Qiwei
We study the nonequilibrium steady state of a stochastic lattice gas model, originally proposed by Katz, Lebowitz and Spohn (Phys. Rev. B 28: 1655 (1983)). Firstly, we solve the model on some small lattices exactly in order to see the general dependence of the steady state upon different parameters of the model. Nextly, we derive some analytical results for infinite lattice systems by taking some suitable limits. We then present some renormalization group results for the continuum version of the model via field theoretical techniques, the supersymmetry of the critical dynamics in zero field is also explored. Finally, we report some very recent 3-D Monte Carlo simulation results, which have been obtained by applying Multi-Spin-Coding techniques on a CDC vector supercomputer - Cyber 205 at John von Neumann Center.
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We 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. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
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.
A stochastic killing system for biological containment of Escherichia coli
DEFF Research Database (Denmark)
Klemm, P.; Jensen, Lars Bogø; Molin, Søren
1995-01-01
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...... a culture of E. coli harboring the plasmid comprising the containment system is left as stationary cells in suspension without nutrients, viability drops exponentially over a period of several days, in contrast to the control cells, which maintain viability nearly unaffected during the same period of time....... Similar results were obtained with a strain in which the killing cassette was inserted in the chromosome. In competition with noncontained cells during growth, the contained cells are always outcompeted. Stochastic killing obtained by the fim-gef fusion is at present relevant only as a containment...
Stochastic Resonance in a Bistable System Subject to Dichotomous Noise
Institute of Scientific and Technical Information of China (English)
ZHOU Yu-Rong; PAN Hui-Mei; GUO Feng; PANG Xiao-Feng
2008-01-01
The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise (DN) is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-to-noise ratio (SNR) and the spectral power amplification (SPA) have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.
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.
Study on phase synchronization of stochastic chaotic system
Institute of Scientific and Technical Information of China (English)
Yang Xiao-Li; Xu Wei
2008-01-01
This paper detects and characterizes the diverse roles played by bounded noise in chaotic phase synchronization (CPS) of weakly coupled nonlinear stochastic systems. Analysis of a paradigmatic model of two bidirectional coupled three-level food chains is carried out by various statistical measures such as Shannon entropy and mutual information. The results indicate that inside the synchronous regime, CPS is considerably reduced under the influence of bounded noise; near the onset of phase synchronization, temporal phase locking is diversely changed with the increase of noise, i.e., either weak or strong noise also degrades the degree of CPS, while intermediate noise enhances CPS remarkably, and an optimal noise intensity is detected that maximizes the enhancement.
Institute of Scientific and Technical Information of China (English)
Hongheng LI; Qi L(U)
2012-01-01
The authors establish the null controllability for some systems coupled by two backward stochastic heat equations.The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
Computing the optimal path in stochastic dynamical systems.
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-08-01
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.
Identification and estimation algorithm for stochastic neural system. II.
Nakao, M; Hara, K; Kimura, M; Sato, R
1985-01-01
The algorithm for identifying the stochastic neural system and estimating the system process which reflects the dynamics of the neural network are presented in this paper. The analogous algorithm has been proposed in our preceding paper (Nakao et al., 1984), which was based on the randomly missed observations of a system process only. Since the previous algorithm mentioned above was subject to an unfavorable effect of consecutively missed observations, to reduce such an effect the algorithm proposed here is designed additionally to observe an intensity process in a neural spike train as the information for the estimation. The algorithm is constructed with the extended Kalman filters because it is naturally expected that a nonlinear and time variant structure is necessary for the filters to realize the observation of an intensity process by means of mapping from a system process to an intensity process. The performance of the algorithm is examined by applying it to some artificial neural systems and also to cat's visual nervous systems. The results in these applications are thought to prove the effectiveness of the algorithm proposed here and its superiority to the algorithm proposed previously.
Computing the optimal path in stochastic dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora [Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, New Jersey 07043 (United States)
2016-08-15
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.
Robust Passivity and Feedback Design for Nonlinear Stochastic Systems with Structural Uncertainty
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper discusses the robust passivity and global stabilization problems for a class of uncertain nonlinear stochastic systems with structural uncertainties. A robust version of stochastic Kalman-Yakubovitch-Popov (KYP lemma is established, which sustains the robust passivity of the system. Moreover, a robust strongly minimum phase system is defined, based on which the uncertain nonlinear stochastic system can be feedback equivalent to a robust passive system. Following with the robust passivity theory, a global stabilizing control is designed, which guarantees that the closed-loop system is globally asymptotically stable in probability (GASP. A numerical example is presented to illustrate the effectiveness of our results.
Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.
Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong
2014-12-01
In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.
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.
Stochastic Predator-Prey System Subject to Lévy Jumps
Directory of Open Access Journals (Sweden)
Xinzhu Meng
2016-01-01
Full Text Available This paper investigates a new nonautonomous impulsive stochastic predator-prey system with the omnivorous predator. First, we show that the system has a unique global positive solution for any given initial positive value. Second, the extinction of the system under some appropriate conditions is explored. In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. Simulations are also carried out to illustrate our theoretical analysis conclusions.
A remark on symmetry of stochastic dynamical systems and their conserved quantities
Albeverio, Sergio A; Albeverio, Sergio; Fei, Shao Ming
1995-01-01
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given by applying symmetry operators to known conserved quantities. Some detailed examples are presented.
Stochastic Resource Allocation for Energy-Constrained Systems
Directory of Open Access Journals (Sweden)
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.
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.
Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay
Institute of Scientific and Technical Information of China (English)
Zhang Aiqing; Fang Huajing
2008-01-01
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.
An integration factor method for stochastic and stiff reaction–diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Ta, Catherine; Wang, Dongyong; Nie, Qing, E-mail: qnie@uci.edu
2015-08-15
Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction–diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction–diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction–diffusion equations arising from models in biology and physical sciences.
Karachanskaya, Elena
2012-01-01
Investigate the stochastic dynamic non-linear system with the Wiener and the Poisson perturbations. For such systems we construct the program control with probability one, which allows this system to move on the given trajectory. In this case the control program is solution of the algebraic system of linear equations. Considered algorithm is based on the first integral theory for stochastic differential equations system.
Filtering nonlinear dynamical systems with linear stochastic models
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
Institute of Scientific and Technical Information of China (English)
CHANG Hong; RU Feng; XUE Jun-yi
2006-01-01
In this paper, data streams are classified into four types conforming to a standardized infrastructure of communication networks for a substation automation system (SAS) based on IEC61850 system. The data exchanged on the net are demonstrated to be stochastic according to investigation on the Ethernet communication principles. Four generalized stochastic Petri nets (GSPN) based models for performance analysis of communication networks of IEC61850 system are developed based on the three-level structure of SAS, different time requirements of the four data streams and different networks topology for different voltage level. The GSPN-based model associated with immediate and exponential transitions is proven to be theoretically isomorphic with Markov chain; hence we apply the mathematic methods of performance evaluation contained in Markov chain to the GSPN models proposed. The computer simulation of the model including only sample value data streams shows that it can meet performance evaluation needs of communication networks of IEC61850 system. Further researches should be focused on the performance of the other three models to explain clear how those different data streams are interrelated to and interact on each other.
Some applications of stochastic averaging method for quasi Hamiltonian systems in physics
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Many physical systems can be modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems can be applied to yield reasonable approximate response sta-tistics.In the present paper,the basic idea and procedure of the stochastic averaging method for quasi Hamiltonian systems are briefly introduced.The applications of the stochastic averaging method in studying the dynamics of active Brownian particles,the reaction rate theory,the dynamics of breathing and denaturation of DNA,and the Fermi resonance and its effect on the mean transition time are reviewed.
Non-Markovian Fermionic Stochastic Schr\\"{o}dinger Equation for Open System Dynamics
Shi, Wufu; Yu, Ting
2012-01-01
In this paper we present an exact Grassmann stochastic Schr\\"{o}dinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic approach to derive the exact master equation for a fermionic system strongly coupled to electronic reservoirs. The generality and applicability of this Grassmann stochastic approach is justified and exemplified by several quantum open system problems concerning quantum decoherence and quantum transport for both vacuum and finite-temperature fermionic reservoirs. We show that the quantum coherence property of the quantum dot system can be profoundly modified by the environment memory.
Institute of Scientific and Technical Information of China (English)
Ronghua Huan; Lincong Chen; Weiliang Jin; Weiqiu Zhu
2009-01-01
An optimal vibration control strategy for partially observable nonlinear quasi Hamil-tonian systems with actuator saturation is proposed. First, a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Ito stochas-tic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.
Some applications of stochastic averaging method for quasi Hamiltonian systems in physics
Institute of Scientific and Technical Information of China (English)
DENG MaoLin; ZHU WeiQiu
2009-01-01
Many physical systems can be modeled as quasi-Hamiltonian systems and the stochastic averaging method for uasi-Hamiltonian systems can be applied to yield reasonable approximate response sta-tistics. In the present paper, the basic idea and procedure of the stochastic averaging method for quasi Hamiltonian systems are briefly introduced. The applications of the stochastic averaging method in studying the dynamics of active Brownian particles, the reaction rate theory, the dynamics of breathing and denaturation of DNA, and the Fermi resonance and its effect on the mean transition time are re-viewed.
Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
Directory of Open Access Journals (Sweden)
Xiaojun Liu
2014-01-01
Full Text Available The Hopf bifurcation of a fractional-order Van der Pol (VDP for short system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.
Estimation and Analysis of Nonlinear Stochastic Systems. Ph.D. Thesis
Marcus, S. I.
1975-01-01
The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.
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
Jarzynski, Christopher
2017-01-01
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.
Fast cooling for a system of stochastic oscillators
Chen, Yongxin; Georgiou, Tryphon T.; Pavon, Michele
2015-11-01
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.
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.
Control of stochastic resonance in bistable systems by using periodic signals
Institute of Scientific and Technical Information of China (English)
Lin Min; Fang Li-Min; Zheng Yong-Jun
2009-01-01
According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctu-ations 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.
On the stabilization of switched linear stochastic systems with unobservable switching laws
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper is concerned with the stabilization problem of switched linear stochastic systems with unobservable switching laws. In this paper the system switches among a finite family of linear stochastic systems. Since there are noise perturbations, the switching laws can not be identified in any finite time horizon. We prove that if each individual subsystem is controllable and the switching duration uniformly has a strict positive lower bound, then the system can be stabilized by using a controller that uses online state estimation.
Variance decomposition in stochastic simulators
Le Maître, O. P.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
2004-01-01
A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed.The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter
Institute of Scientific and Technical Information of China (English)
Xu Wei; Ma Shao-Juan; Xie Wen-Xian
2008-01-01
Stochastic period-doubling bifurcation is explored in a forced Duiting system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
2004-01-01
A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Resonant Phenomenon in a Stochastic Delayed Bistable Chemical System
Li, Chunxuan; Yang, Tao
2015-06-01
In this paper, the resonant phenomenon for a bistable chemical system in the presence of noises and delayed feedback is investigated. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced additively (or multiplicatively). The impacts of the parameter μ of the reaction, time delay τ, strength K of the feedback loop, multiplicative ( D) and additive ( Q) noise strengths and cross-correlation strength λ between two noises on the SNR are discussed. When the periodic signal is introduced additively, our results show (i) the SNR as a function of the parameter μ exhibits a maximum, the existence of the maximum is a characteristic of the parametric resonance (PR) phenomenon; (ii) the SNR as a function of D exhibits only a maximum, however, for the case of SNR as a function of Q exhibits not only a maximum, but also a minimum. The existence of the maximum and minimum in the SNR is the identifying characteristics of the stochastic resonance (SR) and reverse-resonance (RR); and (iii) the increases of τ, K and λ enhance the SR and weaken the RR. Finally, we compare the resonant phenomenon for the additive periodic signal with that for multiplicative one in the chemical system.
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.
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.
Robust H∞ control for uncertain stochastic saturating systems with time delays
Institute of Scientific and Technical Information of China (English)
谢立; 何星; 张卫东; 许晓鹏
2004-01-01
The robust H∞ control problem for uncertain stochastic time-delay systems containing nonlinear actuators is considered. The uncertainties in the systems are assumed to satisfy specific match condition. The time delays exitst in state as well as control input. The new stochastic robust stabilization criterion and a sufficient condition for the existence of stochastic robust stabilizing control law are derived. The delay-independent memoryless robust H∞ controllers are constructed to stabilize the given systems in terms of a group of linear matrix inequalities. A numerical simulation example is presented to show that the proposed approach is valid.
Luenberger-Type Observer Design for Stochastic Time-Delay Systems
Wu, Gang; Li, Long-Suo; Miao, Xiu-Feng; Cong, Xin-Rong
2013-06-01
This paper deals with the problem of an observer design for stochastic time-delay systems. The system states are unmeasured. We derive delay-dependent LMI criteria by means of the Leibniz-Newton formula, the Itô's differential operator and stochastic Lyapunov stability theory in order to obtain sufficient conditions for the asymptotic stability in the mean square for the closed-loop stochastic time-delay system. The proposed conditions are easily and numerically tractable via a Matlab LMI toolbox. The effectiveness of the control strategy is verified by numerical experiments.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
Zeng, Caibin; Yang, Qigui
2015-12-01
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.
Energy Technology Data Exchange (ETDEWEB)
Subalakshmi, R. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: suba.ab.bu@gmail.com; Balachandran, K. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: balachandran_k@lycos.com
2009-11-30
Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.
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.
Energy Technology Data Exchange (ETDEWEB)
Berg, J. S. [Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.
2015-05-03
I describe a generic formulation for the evolution of emittances and lattice functions under arbitrary, possibly non-Hamiltonian, linear equations of motion. The average effect of stochastic processes, which would include ionization interactions and synchrotron radiation, is also included. I first compute the evolution of the covariance matrix, then the evolution of emittances and lattice functions from that. I examine the particular case of a cylindrically symmetric system, which is of particular interest for ionization cooling.
Stochastic Stability of Sampled Data Systems with a Jump Linear Controller
Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven
2004-01-01
In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.
Directory of Open Access Journals (Sweden)
Na Duan
2012-01-01
Full Text Available The adaptive stabilization scheme based on tuning function for stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS inverse dynamics is investigated. By combining the stochastic LaSalle theorem and small-gain type conditions on SiISS, an adaptive output feedback controller is constructively designed. It is shown that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally stable in probability.
Institute of Scientific and Technical Information of China (English)
QUAN Ji; WANG Xian-Jia
2013-01-01
Traditional evolutionary games assume uniform interaction rate,which means that the rate at which individuals meet and interact is independent of their strategies.But in some systems,especially biological systems,the players interact with each other discriminately.Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies.Their model is based on replicator dynamics which assumes an infinite size population.But in reality,the number of individuals in the population is always finite,and there will be some random interference in the individuals' strategy selection process.Therefore,it is more practical to establish the corresponding stochastic evolutionary model in finite populations.In fact,the analysis of evolutionary games in a finite size population is more difficult.Just as Taylor and Nowak said in the outlook section of their paper,"The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations." In this paper,we are exactly doing this work.We extend Taylor and Nowak's model from infinite to finite case,especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system.We model the strategy evolutionary process of the population by a continuous ergodic Markov process.Based on the fimit distribution of the process,we can give the evolutionary stable state of the system.We make a complete classification of the symmetric 2 × 2 games.For each case game,the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough.In contrast with most literatures in evolutionary games using the simulation method,all our results obtained are analytical.Especially,in the dominant-case game,coexistence of the two strategies may become evolutionary stable states in our model.This result can be used to explain the emergence of
Modeling of uncertain spectra through stochastic autoregressive systems
Wang, Yiwei; Wang, X. Q.; Mignolet, Marc P.; Yang, Shuchi; Chen, P. C.
2016-03-01
The focus of this investigation is on the formulation and validation of a modeling strategy of the uncertainty that may exist on the specification of the power spectral density of scalar stationary processes and on the spectral matrices of vector ones. These processes may, for example, be forces on a structure originating from natural phenomena which are coarsely modeled (i.e., with epistemic uncertainty) or are specified by parameters unknown (i.e., with aleatoric uncertainty) in the application considered. The propagation of the uncertainty, e.g., to the response of the structure, may be carried out provided that a stochastic model of the uncertainty in the power spectral density/matrix is available from which admissible samples can be efficiently generated. Such a stochastic model will be developed here through an autoregressive-based parameterization of the specified baseline power spectral density/matrix and of its random samples. Autoregressive (AR) models are particularly well suited for this parametrization since their spectra are known to converge to a broad class of spectra (all non-pathological spectra) as the AR order increases. Note that the characterization of these models is not achieved directly in terms of their coefficients but rather in terms of their reflection coefficients which lie (or their eigenvalues in the vector process case) in the domain [0,1) as a necessary and sufficient condition for stability. Maximum entropy concepts are then employed to formulate the distribution of the reflection coefficients in both scalar and vector process case leading to a small set of hyperparameters of the uncertain model. Depending on the information available, these hyperparameters could either be varied in a parametric study format to assess the effects of uncertainty or could be identified, e.g., in a maximum likelihood format, from observed data. The validation and assessment of these concepts is finally achieved on several examples including the
Going with the flow: enhancing stochastic switching rates in multi-gyre systems
Heckman, Christoffer R; Schwartz, Ira B
2014-01-01
A control strategy is employed that modifies the stochastic escape times from one basin of attraction to another in a model of a double-gyre flow. The system studied captures the behavior of a large class of fluid flows that circulate and have multiple almost invariant sets. In the presence of noise, a particle in one gyre may randomly switch to an adjacent gyre due to a rare large fluctuation. We show that large fluctuation theory may be applied for controlling autonomous agents in a stochastic environment, in fact leveraging the stochastic- ity to the advantage of switching between regions of interest and concluding that patterns may be broken or held over time as the result of noise. We demonstrate that a controller can effectively manipulate the probability of a large fluctuation, thereby modifying escape times exponentially; this demonstrates the potential of optimal control strategies that work in combination with the endemic stochastic environment. To demonstrate this, stochastic simulations and numeri...
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.
Model reduction for stochastic chemical systems with abundant species
Energy Technology Data Exchange (ETDEWEB)
Smith, Stephen; Cianci, Claudia; Grima, Ramon [School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH93JR, Scotland (United Kingdom)
2015-12-07
Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.
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.
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Liu, Chao; Wang, Luping; Zhang, Qingling; Yan, Yun
2017-09-01
This paper presents a double delayed bioeconomic phytoplankton zooplankton system with commercial harvesting on zooplankton and environmental stochasticity. Maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered. Environmental stochasticity is incorporated into the proposed system in form of Gaussian white noises. Some sufficient conditions are derived to show that the proposed system has a unique global positive solution. In absence of double time delays, stochastic stability and existence of stochastic Hopf bifurcation are studied based on invariant measure theory and singular boundary theory of diffusion process for the proposed system. In presence of double time delays, asymptotic behaviors of the interior equilibrium are discussed by constructing some appropriate Lyapunov functions.
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.
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...... by a continuous-time stochastic process. The main result of this paper is that we may identify the realizations of the global dynamics with the solutions of a differential inclusion. Hence, an analysis of switched systems with switching noise can be carried out either based on a non-deterministic method via...... the differential inclusion, or on a stochastic method via the stochastic process. Furthermore, we describe how to construct intensity plots, which provide a quick overview of the behavior of the system. An example is included to illustrate this....
Levin, Pavel; Lefebvre, Jérémie; Perkins, Theodore J
2012-12-07
Many biomolecular systems depend on orderly sequences of chemical transformations or reactions. Yet, the dynamics of single molecules or small-copy-number molecular systems are significantly stochastic. Here, we propose state sequence analysis--a new approach for predicting or visualizing the behaviour of stochastic molecular systems by computing maximum probability state sequences, based on initial conditions or boundary conditions. We demonstrate this approach by analysing the acquisition of drug-resistance mutations in the human immunodeficiency virus genome, which depends on rare events occurring on the time scale of years, and the stochastic opening and closing behaviour of a single sodium ion channel, which occurs on the time scale of milliseconds. In both cases, we find that our approach yields novel insights into the stochastic dynamical behaviour of these systems, including insights that are not correctly reproduced in standard time-discretization approaches to trajectory analysis.
One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters
Directory of Open Access Journals (Sweden)
Taras Lukashiv
2016-01-01
Full Text Available The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.
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
Stochastic Verification Theorem of Forward-Backward Controlled System for Viscosity Solutions
Zhang, Liangquan
2010-01-01
In this paper, we investigate the controlled system described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generater of BSDE. A new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions. It is worth to pointing out that this theorem has wider applicability than the restrictive classical verification theorems. As a relevant problem, the optimal stochastic feedback controls for forward-backward system are discussed as well.
P-th moment and almost sure stability of stochastic switched nonlinear systems.
Gu, Haibo; Gao, Caixia
2016-01-01
This paper mainly tends to utilize [Formula: see text]-type function to investigate p-th moment and almost sure stability for a class of stochastic switched nonlinear systems. Based on the multiple Lyapunov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the proposed results.
Workshop on quantum stochastic differential equations for the quantum simulation of physical systems
2016-09-22
SECURITY CLASSIFICATION OF: This is a report on the “Workshop on quantum stochastic differential equations for the quantum simulation of physical ...mathematical tools to the quantum simulation of physical systems of interest to the Army. There were participants from US Government agencies, industry, and... quantum stochastic differential equations for the quantum simulation of physical systems Report Title This is a report on the “Workshop on quantum
Control design for discrete-time state-multiplicative noise stochastic systems
Krokavec, Dušan; Filasová, Anna
2015-11-01
Design conditions for existence of the H∞ linear state feedback control for discretetime stochastic systems with state-multiplicative noise and polytopic uncertainties are presented in the paper. Using an enhanced form of the bounded real lemma for discrete-time stochastic systems with state-multiplicative noise, the LMI-based procedure is provided for computation of the gains of linear, as well as nonlinear, state control law. The approach is illustrated on an example demonstrating the validity of the proposed method.
Exact rule-based stochastic simulations for the system with unlimited number of molecular species
Bernatskiy, Anton V
2016-01-01
We introduce expandable partial propensity direct method (EPDM) - a new exact stochastic simulation algorithm suitable for systems involving many interacting molecular species. The algorithm is especially efficient for sparsely populated systems, where the number of species that may potentially be generated is much greater than the number of species actually present in the system at any given time. The number of operations per reaction scales linearly with the number of species, but only those which have one or more molecules. To achieve this kind of performance we are employing a data structure which allows to add and remove species and their interactions on the fly. When a new specie is added, its interactions with every other specie are generated dynamically by a set of user-defined rules. By removing the records involving the species with zero molecules, we keep the number of species as low as possible. This enables simulations of systems for which listing all species is not practical. The algorithm is ba...
Consalvi, Jean-Louis
2017-01-01
The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as `absorption Turbulence Radiation Interaction (TRI)' and `emission TRI'. Emission TRI is related to the non-linear coupling between fluctuations of the absorption coefficient and fluctuations of the Planck function and can be described without introduction any approximation by using a transported PDF method. In this study, a hybrid flamelet/ Stochastic Eulerian Field Model is used to solve the transport equation of the one-point one-time PDF. In this formulation, the steady laminar flamelet model (SLF) is coupled to a joint Probability Density Function (PDF) of mixture fraction, enthalpy defect, scalar dissipation rate, and soot quantities and the PDF transport equation is solved by using a Stochastic Eulerian Field (SEF) method. Soot production is modeled by a semi-empirical model and the spectral dependence of the radiatively participating species, namely combustion products and soot, are computed by using a Narrow Band Correlated-k (NBCK) model. The model is applied to simulate an ethylene/methane turbulent jet flame burning in an oxygen-enriched environment. Model results are compared with the experiments and the effects of taken into account Emission TRI on flame structure, soot production and radiative loss are discussed.
L{sup 1} group consensus of multi-agent systems with switching topologies and stochastic inputs
Energy Technology Data Exchange (ETDEWEB)
Shang, Yilun, E-mail: shylmath@hotmail.com [Institute for Cyber Security, University of Texas at San Antonio, TX 78249 (United States); SUTD-MIT International Design Center, Singapore University of Technology and Design, Singapore 138682 (Singapore)
2013-10-01
Understanding how interacting subsystems of an overall system lead to cluster/group consensus is a key issue in the investigation of multi-agent systems. In this Letter, we study the L{sup 1} group consensus problem of discrete-time multi-agent systems with external stochastic inputs. Based on ergodicity theory and matrix analysis, L{sup 1} group consensus criteria are obtained for multi-agent systems with switching topologies. Some numerical examples are provided to illustrate the effectiveness and feasibility of the theoretical results.
Institute of Scientific and Technical Information of China (English)
SONG Li-Na; ZHANG Hong-Qing
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Trindade, Bruno Machado; Campos, Tarcisio Passos Ribeiro de, E-mail: campos@nuclear.ufmg.b [Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG (Brazil). Program of Post-Graduation in Sciences and Nuclear Techniques
2011-03-15
Objective: The present paper describes a procedure for conversion of computed tomography or magnetic resonance images into a three-dimensional voxel model for dosimetry purposes. Such model is a personalized representation of the patient that can be utilized in nuclear particle transport simulations by means of the MCNP (Monte Carlo N-Particle) code, reproducing the stochastic process of nuclear particles interaction with human tissues. Materials and Methods: The developed computational system - SISCODES - is a tool designed for 3D planning of radiotherapy or radiological procedures. Based on tomographic images of the patient, the treatment plan is modeled and simulated. Then, the absorbed doses are shown by means of isodose curves superimposed on the model. The SISCODES couples the three dimensional model with the MCNP5 code, simulating the protocol of exposure to ionizing radiation. Results: The SISCODES has been utilized by the NRI/CNPq in the creation of anthropomorphic and anthropometric voxel models which are coupled with the MCNP code for modeling brachytherapy and teletherapy applied to lung, pelvis, spine, head and neck tumors, among others. The current SISCODES modules are presented together with examples of cases of radiotherapy planning. Conclusion: The SISCODES provides a fast method to create personalized voxel models of any patient which can be used in stochastic simulations. The combination of the MCNP simulation with a personalized model of the patient increases the dosimetry accuracy in radiotherapy. (author)
Stochastic Hall-Magneto-hydrodynamics System in Three and Two and a Half Dimensions
Yamazaki, Kazuo
2017-01-01
We introduce the stochastic Hall-magneto-hydrodynamics (Hall-MHD) system in three and two and a half dimensions with infinite-dimensional multiplicative noise, white in time, and prove the global existence of a martingale solution via a stochastic Galerkin approximation and applications of Prokhorov's, Skorokhod's and martingale representation theorems, as well as the pressure term through de Rham's theorem adapted to processes. The Hall term represents mathematically a very singular nonlinear term, unprecedented in the previous work. The results extend many others on the deterministic Hall-MHD and stochastic MHD systems and Navier-Stokes equations. In contrast to the stochastic MHD system, the path-wise uniqueness in the two and a half dimensional case is an open problem.
Energy Technology Data Exchange (ETDEWEB)
Kryvohuz, Maksym, E-mail: mkryvohu@uci.edu; Mukamel, Shaul [Chemistry Department, University of California, Irvine, California 92697-2025 (United States)
2015-06-07
Generalized nonlinear response theory is presented for stochastic dynamical systems. Experiments in which multiple measurements of dynamical quantities are used along with multiple perturbations of parameters of dynamical systems are described by generalized response functions (GRFs). These constitute a new type of multidimensional measures of stochastic dynamics either in the time or the frequency domains. Closed expressions for GRFs in stochastic dynamical systems are derived and compared with numerical non-equilibrium simulations. Several types of perturbations are considered: impulsive and periodic perturbations of temperature and impulsive perturbations of coordinates. The present approach can be used to study various types of stochastic processes ranging from single-molecule conformational dynamics to chemical kinetics of finite-size reactors such as biocells.
Diffusion in stochastically and periodically modulated Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Bazzani, A.; Siboni, S.; Turchetti, G. [Dipartimento di Fisica della Universita di Bologna, ITALY and INFN Sezione di Bologna (ITALY)
1995-09-01
We consider an area preserving map whose linear frequency is stochastically perturbed. When no low order resonances are present a Fokker-Planck equation for the action diffusion is written and its solution agrees with the simulation of the process. The key point is the description of the map with an interpolating hamiltonian for which the action diffusion coefficient can be analytically computed. When the frequency has a slow periodic modulation, then for low amplitudes the diffusion is limited to the action interval swept by a chain of islands, whereas for large amplitudes the diffusion reaches the dynamic aperture as in the stochastic case.
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-14
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.
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.
2017-05-01
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.
Directory of Open Access Journals (Sweden)
Yan Che
2012-01-01
Full Text Available The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time-varying delays and missing measurements. The considered distributed time-varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean-square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.
Integral characteristics: a key to understanding structure formation in stochastic dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Klyatskin, Valery I, E-mail: klyatskin@yandex.ru
2011-05-31
Some general problems concerning the stochastic approach are discussed in relation to parametrically excited stochastic dynamic systems described by partial differential equations. Such problems arise in hydrodynamics, magnetohydrodynamics, and astro, plasma, and radio physics and share the feature that the statistical characteristics of their solutions (moments, correlation and spectral functions, and so on) increasing exponentially with time, whereas some solution implementations lead to the formation of random structures with probability one as a result of clustering. The goal of this paper is to use the ideas of stochastic topography to find conditions under which such structures arise. (reviews of topical problems)
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.
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Energy Technology Data Exchange (ETDEWEB)
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi, E-mail: thfan@engr.uconn.edu [Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139 (United States); Tuinier, Remco [Van' t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Department of Chemistry, Utrecht University, Padualaan 8, 3584 CH, Utrecht (Netherlands); DSM ChemTech R and D, P.O. Box 18, 6160 MD Geleen (Netherlands); Taniguchi, Takashi [Graduate School of Engineering, Kyoto University Katsura Campus, Nishikyo-ku, Kyoto 615-8510 (Japan)
2014-06-07
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.
On square-wave-driven stochastic resonance for energy harvesting in a bistable system
Directory of Open Access Journals (Sweden)
Dongxu Su
2014-11-01
Full Text Available 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
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.
The Geometry of Stochastic Reduction of an Entangled System
Belenkiy, A; Shnider, S; Belenkiy, Ari; Horwitz, Lawrence; Shnider, Steve
2006-01-01
We show that the method of stochastic reduction of linear superpositions can be applied to the process of disentanglement for the spin-0 state of two spin-1/2 particles. We describe the geometry of this process in the framework of the complex projective space
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.
IDENTIFICATION OF BOTH CLOSED- AND OPEN-LOOP STOCHASTIC SYSTEM WHILE STABILIZING IT
Institute of Scientific and Technical Information of China (English)
CHEN Hanfu (Han-Fu Chen)
2002-01-01
This paper proposes a recursive algorithm estimating coefficients of thc linear stochastic control system (ARX system) driven by a martingale difference sequence, while adaptively stabilizing the system without introducing external excitation signal. The system is allowed to be unstable and of nonminimum-phase. The estimates derived for the coefficients of both closed-loop and open-loop systems are strongly consistent.
Stochastic Multi-Resonance in a Linear System Driven by Multiplicative Polynomial Dichotomous Noise
Institute of Scientific and Technical Information of China (English)
ZHANG Lu; ZHONG Su-Chuan; PENG Hao; LUO Mao-Kang
2011-01-01
We investigate stochastic resonance in a linear system subjected to multiplicative noise that is a polynomial function of colored noise. Using the stochastic averaging method, the analytical expression of the output signal-to-noise ratio (SNR) is derived. Theoretical analysis and numerical results show that the output SNR is a nonmonotonic function of both the noise intensity and the correlation rate. Moreover, the phenomoenon of stochastic multi-resonance (SMR) is found, which is not observed in conventional linear systems driven by multiplicative noise with only a linear term.%@@ We investigate stochastic resonance in a linear system subjected to multiplicative noise that is a polynomial function of colored noise.Using the stochastic averaging method,the analytical expression of the output signalto-noise ratio(SNR)is derived.Theoretical analysis and numerical results show that the output SNR is a nonmonotonic function of both the noise intensity and the correlation rate.Moreover,the phenomoenon of stochastic multi-resonance(SMR)is found,which is not observed in conventional linear systems driven by multiplicative
Accelerated stochastic and hybrid methods for spatial simulations of reaction-diffusion systems
Rossinelli, D; Bayati, B; Koumoutsakos, P.
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial т-Leaping (Sт -Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid т-Leaping (Hт-Leaping), combining a deterministic diffusion approximation with a т-Leaping acceleration of the stochastic reactions. The algorithms are v...
MATHEMATICAL FRAMEWORK FOR THE ANALYSIS OF DYNAMC STOCHASTIC SYSTEMS WITH THE RAVEN CODE
Energy Technology Data Exchange (ETDEWEB)
C. Rabiti; D. Mandelli; J. Cogliati; R. Kinoshita
2013-05-01
RAVEN (Reactor Analysis and Virtual control Environment) is a software code under development at Idaho National Laboratory aimed at performing probabilistic risk assessment and uncertainty quantification using RELAP-7, for which it acts also as a simulation controller. In this paper we will present the equations characterizing a dynamic stochastic system and we will then discuss the behavior of each stochastic term and how it is accounted for in the RAVEN software design. Moreover we will present preliminary results of the implementation.
Non-linear stochastic optimal control of acceleration parametrically excited systems
Wang, Yong; Jin, Xiaoling; Huang, Zhilong
2016-02-01
Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.
Juricke, Stephan; Jung, Thomas
2014-06-28
The influence of a stochastic sea ice strength parametrization on the mean climate is investigated in a coupled atmosphere-sea ice-ocean model. The results are compared with an uncoupled simulation with a prescribed atmosphere. It is found that the stochastic sea ice parametrization causes an effective weakening of the sea ice. In the uncoupled model this leads to an Arctic sea ice volume increase of about 10-20% after an accumulation period of approximately 20-30 years. In the coupled model, no such increase is found. Rather, the stochastic perturbations lead to a spatial redistribution of the Arctic sea ice thickness field. A mechanism involving a slightly negative atmospheric feedback is proposed that can explain the different responses in the coupled and uncoupled system. Changes in integrated Antarctic sea ice quantities caused by the stochastic parametrization are generally small, as memory is lost during the melting season because of an almost complete loss of sea ice. However, stochastic sea ice perturbations affect regional sea ice characteristics in the Southern Hemisphere, both in the uncoupled and coupled model. Remote impacts of the stochastic sea ice parametrization on the mean climate of non-polar regions were found to be small.
Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching
Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven
2004-01-01
This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.
2017-03-30
AFRL-AFOSR-VA-TR-2017-0075 Stochastic Hybrid Systems Modeling and Middleware-enabled DDDAS for Next-generation US Air Force Systems Aniruddha...release. Air Force Research Laboratory AF Office Of Scientific Research (AFOSR)/RTA2 4/6/2017https://livelink.ebs.afrl.af.mil/livelink/llisapi.dll a...Sep 2013 to 31 Dec 2016 4. TITLE AND SUBTITLE Stochastic Hybrid Systems Modeling and Middleware-enabled DDDAS for Next- generation US Air Force
SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN IRn
Institute of Scientific and Technical Information of China (English)
TANG SHANJIAN
2005-01-01
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-10-01
We study a stochastic dynamics of systems with hard excitement of auto-oscillations possessing a bistability mode with coexistence of the stable equilibrium and limit cycle. A principal difference in the results of the impact of additive and parametric random disturbances is shown. For the stochastic van der Pol oscillator with increasing parametric noise, qualitative transformations of the probability density function form "crater"-"peak+crater"-"peak" are demonstrated by numerical simulation. An analytical investigation of such P bifurcations is carried out for the stochastic Hopf-like model with hard excitement of self-oscillations. A detailed parametric description of the response of this model on the additive and multiplicative noise and corresponding stochastic bifurcations are presented and discussed.
COMPUTER DATA ANALYSIS AND MODELING: COMPLEX STOCHASTIC DATA AND SYSTEMS
2010-01-01
This collection of papers includes proceedings of the Ninth International Conference “Computer Data Analysis and Modeling: Complex Stochastic Data and Systems” organized by the Belarusian State University and held in September 2010 in Minsk. The papers are devoted to the topical problems: robust and nonparametric data analysis; statistical analysis of time series and forecasting; multivariate data analysis; design of experiments; statistical signal and image processing...
Balls, cups, and quasi-potentials: quantifying stability in stochastic systems.
Nolting, Ben C; Abbott, Karen C
2016-04-01
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic regime shifts. The probability, frequency, duration, and dynamics of these shifts will all depend on the relative stability of the stable states. Unfortunately, the concept of "stability" in ecology has suffered from substantial confusion and this is particularly problematic for systems where stochastic perturbations can cause shifts between coexisting alternative stable states. A useful way to visualize stable states in stochastic systems is with a ball-in-cup-diagram, in which the state of the system is represented as the position of a ball rolling on a surface, and the random perturbations can push the ball from one basin of attraction to another. The surface is determined by a potential function, which provides a natural stability metric. Systems amenable to this representation, called gradient systems, are quite rare, however. As a result, the potential function is not widely used and other approaches based on linear stability analysis have become standard. Linear stability analysis is designed for local analysis of deterministic systems and, as we show, can produce a highly misleading picture of how the system will behave under continual, stochastic perturbations. In this paper, we show how the potential function can be generalized so that it can be applied broadly, employing a concept from stochastic analysis called the quasi-potential. Using three classic ecological models, we demonstrate that the quasi-potential provides a useful way to quantify stability in stochastic systems. We show that the quasi-potential framework helps clarify long-standing confusion about stability in stochastic ecological systems, and we argue that ecologists should adopt it as a practical tool for analyzing these systems.
Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method
Directory of Open Access Journals (Sweden)
Pham Luu Trung Duong
2015-01-01
Full Text Available The distributed order concept, which is a parallel connection of fractional order integrals and derivatives taken to the infinitesimal limit in delta order, has been the main focus in many engineering areas recently. On the other hand, there are few numerical methods available for analyzing distributed order systems, particularly under stochastic forcing. This paper proposes a novel numerical scheme for analyzing the behavior of a distributed order linear single input single output control system under random forcing. The method is based on the operational matrix technique to handle stochastic distributed order systems. The existing Monte Carlo, polynomial chaos, and frequency methods were first adapted to the stochastic distributed order system for comparison. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method for the analysis of stochastic distributed order systems. The stability of the systems under stochastic perturbations can also be inferred easily from the moment of random output obtained using the proposed method. Based on the hybrid spectral framework, the optimal design was elaborated on by minimizing the suitably defined constrained-optimization problem.
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...... 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....... 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...
THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
SHANG MEI; GUO YONG-XIN
2001-01-01
We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.
National Research Council Canada - National Science Library
Muhammad Murtadha Othman; Nur Ashida Salim; Ismail Musirin
2017-01-01
.... This paper presents the proposed stochastic event tree technique used to assess the sustainability against the occurrence of dynamic power system blackout emanating from implication of critical...
Directory of Open Access Journals (Sweden)
Angelica María Atehortúa Labrador
2012-09-01
Full Text Available This article describes DSamala toolbox, a computational tool for simulating and analysing discrete, continuous, stochastic dynamic systems; It is presented as a MATLAB toolbox. DSamala toolbox makes a significant contribution to studying dynamic systems through the use of information and communication technology (ICT, especially when equations modelling these systems are difficult or impossible to solve analytically.
A Mean-Variance Criterion for Economic Model Predictive Control of Stochastic Linear Systems
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Dammann, Bernd; Madsen, Henrik;
2014-01-01
Stochastic linear systems arise in a large number of control applications. This paper presents a mean-variance criterion for economic model predictive control (EMPC) of such systems. The system operating cost and its variance is approximated based on a Monte-Carlo approach. Using convex relaxation...
Directory of Open Access Journals (Sweden)
Chunyan Ji
2010-01-01
Full Text Available We discuss a two-species Lotka-Volterra mutualism system with stochastic perturbation. We show that there is a unique nonnegative solution of this system. Furthermore, we investigate that there exists a stationary distribution for this system, and it has ergodic property.
An investigation of setup instability in non-stationary stochastic inventory systems
Kilic, Onur A.; Tarim, S. Armagan
In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments,
Nekton Interaction Monitoring System
Energy Technology Data Exchange (ETDEWEB)
2017-03-15
The software provides a real-time processing system for sonar to detect and track animals, and to extract water column biomass statistics in order to facilitate continuous monitoring of an underwater environment. The Nekton Interaction Monitoring System (NIMS) extracts and archives tracking and backscatter statistics data from a real-time stream of data from a sonar device. NIMS also sends real-time tracking messages over the network that can be used by other systems to generate other metrics or to trigger instruments such as an optical video camera. A web-based user interface provides remote monitoring and control. NIMS currently supports three popular sonar devices: M3 multi-beam sonar (Kongsberg), EK60 split-beam echo-sounder (Simrad) and BlueView acoustic camera (Teledyne).
Energy Technology Data Exchange (ETDEWEB)
Huan, Ronghua; Zhu, Weiqiu [Zhejiang University, Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Hangzhou (China); Wu, Yongjun [East China University of Science and Technology, School of Information Science and Engineering, Shanghai (China)
2009-02-15
A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi nonintegrable-Hamiltonian systems with actuator saturation is proposed. First, an n-degree-of-freedom (n-DOF) controlled quasi nonintegrable-Hamiltonian system is reduced to a partially averaged Ito stochastic differential equation by using the stochastic averaging method for quasi nonintegrable-Hamiltonian systems. Then, a dynamical programming equation is established by using the stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equation. An example of two controlled nonlinearly coupled Duffing oscillators is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and that chattering is reduced significantly compared with the bang-bang control strategy. (orig.)
Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Ronghua Huan; Maolin Deng; Weiqiu Zhu
2007-01-01
In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged Ito stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged Ito equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged Ito equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.
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.
Institute of Scientific and Technical Information of China (English)
LIU Yungang; ZHANG Jifeng
2004-01-01
A minimal-order observer and output-feedback stabilization control are given for single-input multi-output stochastic nonlinear systems with unobservable states, unmodelled dynamics and stochastic disturbances. Based on the observer designed, the estimates of all observable states of the system are given, and the convergence of the estimation errors are analyzed. In addition, by using the integrator backstepping approach,an output-feedback stabilization control is constructively designed, and sufficient conditions are obtained under which the closed-loop system is asymptotically stable in the large or bounded in probability, respectively.
Institute of Scientific and Technical Information of China (English)
Weihai ZHANG; Xuezhen LIU; Shulan KONG; Qinghua LI
2006-01-01
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
New approach to stochastic stability and controller design for networked control systems
Institute of Scientific and Technical Information of China (English)
Shanbin LI; Youxian SUN
2005-01-01
This paper addresses the random time-delays and packet losses issues of networked control systems (NCS) within the framework of jump linear systems with mode-dependent time-delays.A new delay-dependent condition on the stochastic stability is proposed by a new stochastic Lyapunov-Krasovskii functional.The condition is formulated as a set of coupled linear matrix inequalities (LMIs).As an example to verify the proposed method,an inverted-pendulum system with network is considered.The simulation results demonstrate the effectiveness of the method.
Continuous measurement of cardiac output using stochastic system identification techniques.
Yelderman, Mark
2004-01-01
Indicator dilutions techniques offer the most reliable methods of determining clinical cardiac output because of the elastic nature of the cardiac vessels. A catheter-mounted beating filament affords a simple means of supplying "heat" indicator, but is power and temperature limited because of possible patient injury. A stochastic signal processing method using pseudorandom binary infusion of heat offers a process of enhancing the signal to noise sufficiently to facilitate a computation of cardiac output over a reasonable time period (5 min) with a clinically acceptable error.
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.
Passivity and Passification for a Class of Uncertain Switched Stochastic Time-Delay Systems.
Lian, Jie; Shi, Peng; Feng, Zhi
2013-02-01
This paper is concerned with the problems of passivity and passification for a class of uncertain switched systems subject to stochastic disturbance and time-varying delay. The passivity property is adopted to analyze the influence of the external disturbance on such systems to achieve prescribed attenuation levels. Based on average dwell time approach, free-weighting matrix method, and Jensen's integral inequality, delay-dependent sufficient conditions are obtained in terms of linear matrix inequalities, which ensure the uncertain switched stochastic time-delay system to be robustly mean-square exponentially stable and stochastically passive. Then, the switched passive controllers are synthesized by linearization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.
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.
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.
Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki
2008-06-01
Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.
Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.
Venturi, D; Karniadakis, G E
2014-06-08
Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.
Stochastic volatility models at ρ=±1 as second class constrained Hamiltonian systems
Contreras G., Mauricio
2014-07-01
The stochastic volatility models used in the financial world are characterized, in the continuous-time case, by a set of two coupled stochastic differential equations for the underlying asset price S and volatility σ. In addition, the correlations of the two Brownian movements that drive the stochastic dynamics are measured by the correlation parameter ρ (-1≤ρ≤1). This stochastic system is equivalent to the Fokker-Planck equation for the transition probability density of the random variables S and σ. Solutions for the transition probability density of the Heston stochastic volatility model (Heston, 1993) were explored in Dragulescu and Yakovenko (2002), where the fundamental quantities such as the transition density itself, depend on ρ in such a manner that these are divergent for the extreme limit ρ=±1. The same divergent behavior appears in Hagan et al. (2002), where the probability density of the SABR model was analyzed. In an option pricing context, the propagator of the bi-dimensional Black-Scholes equation was obtained in Lemmens et al. (2008) in terms of the path integrals, and in this case, the propagator diverges again for the extreme values ρ=±1. This paper shows that these similar divergent behaviors are due to a universal property of the stochastic volatility models in the continuum: all of them are second class constrained systems for the most extreme correlated limit ρ=±1. In this way, the stochastic dynamics of the ρ=±1 cases are different of the -1mechanics of the quantum model, implies that stochastic volatility models at ρ=±1 correspond to a constrained system. To study the dynamics in an appropriate form, Dirac's method for constrained systems (Dirac, 1958, 1967) must be employed, and Dirac's analysis reveals that the constraints are second class. In order to obtain the transition probability density or the option price correctly, one must evaluate the propagator as a constrained Hamiltonian path-integral (Henneaux and
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.
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
Directory of Open Access Journals (Sweden)
Anders Gjelsvik
1982-07-01
Full Text Available A first-order differential dynamic programming (DDP algorithm is used for computing optimal control for a five-reservoir system, where the stochastic inflow process has been approximated by a few discrete disturbance values in each time step. The method is found to be faster than linear programming, previously tried on the same system model.
Wind power integration studies using a multi-stage stochastic electricity system model
DEFF Research Database (Denmark)
Meibom, Peter; Barth, R.; Brand, H.;
2007-01-01
A large share of integrated wind power causes technical and financial impacts on the operation of the existing electricity system due to the fluctuating behaviour and unpredictability of wind power. The presented stochastic electricity market model optimises the unit commitment considering four...... kinds of electricity markets (e.g. a spot and balancing market) and taking into account the stochastic behaviour of the wind power generation and of the prediction error. It can be used for the evaluation of varying electricity prices and system costs due to wind power integration...
Institute of Scientific and Technical Information of China (English)
MENG QingXin; TANG MaoNing
2009-01-01
The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel's martingales and an independent multi-dimensional Brownian motion.Necessary and sufficient conditions for an optimal control of the control problem with the control domain being convex are proved by the classical method of convex variation,and the coefficients appearing in the systems are allowed to depend on the control variables.As an application,the linear quadratic stochastic optimal control problem is studied.
On the evaluation of expected performance cost for partially observed closed-loop stochastic systems
Bayard, D. S.; Eslami, M.
1985-01-01
New methods are presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.
An extended phase-space stochastic quantization of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Ter-Kazarian, G T [Byurakan Astrophysical Observatory, Byurakan 378433, Aragatsotn District (Armenia); Sobouti, Y [Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan, PO Box 45195-159 (Iran, Islamic Republic of)], E-mail: gago-50@yahoo.com, E-mail: sobouti@iasbs.ac.ir
2008-08-08
Having gained some insight into the concept of 'actual and virtual paths' in a phase-space formalism (Sobouti and Nasiri 1993 Int. J. Mod. Phys. B 7 3255, Nasiri et al 2006 J. Math. Phys. 47 092106), in the present paper we address the question of 'extended' phase-space stochastic quantization of Hamiltonian systems with first class holonomic constraints. We present the appropriate Langevin equations, which quantize such constrained systems, and prove the equivalence of the stochastic quantization method with the conventional path-integral gauge measure of Faddeev-Popov quantization.
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.
Qian, Min; Zhang, Xue-Juan
2002-03-01
This article investigates the influence of noise in a two-dimensional square array of coupled nonlinear oscillators without periodic driving. Array enhanced stochastic resonance under global as well as local noise perturbation is shown to exist under a crucial condition: the value of the rotation number of the deterministic system being zero. Meanwhile, the stochastic synchronization phenomenon is displayed in a wide range of noise intensity whether noise is added globally or locally. Furthermore, for every oscillator, the peak frequency is shown to agree with the rotation number much better than in the uncoupled system.
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
Liu, Di
2008-10-01
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.
Morshed, Monjur; Ingalls, Brian; Ilie, Silvana
2017-01-01
Sensitivity analysis characterizes the dependence of a model's behaviour on system parameters. It is a critical tool in the formulation, characterization, and verification of models of biochemical reaction networks, for which confident estimates of parameter values are often lacking. In this paper, we propose a novel method for sensitivity analysis of discrete stochastic models of biochemical reaction systems whose dynamics occur over a range of timescales. This method combines finite-difference approximations and adaptive tau-leaping strategies to efficiently estimate parametric sensitivities for stiff stochastic biochemical kinetics models, with negligible loss in accuracy compared with previously published approaches. We analyze several models of interest to illustrate the advantages of our method.
The stochastic system approach to causality with a view toward lifecourse epidemiology
Commenges, Daniel
2012-01-01
The approach of causality based on physical laws and systems is revisited. The issue of "levels", the relevance to epidemiology and the definition of effects are particularly developed. Moreover it is argued that this approach that we call the stochastic system approach is particularly well fitted to study lifecourse epidemiology. A hierarchy of factors is described that could be modeled using a suitable multivariate stochastic process. To illustrate this approach, a conceptual model for coronary heart disease mixing continuous and discrete state-space processes is proposed.
Wind power integration studies using a multi-stage stochastic electricity system model
DEFF Research Database (Denmark)
Meibom, Peter; Barth, R.; Brand, H.
2007-01-01
A large share of integrated wind power causes technical and financial impacts on the operation of the existing electricity system due to the fluctuating behaviour and unpredictability of wind power. The presented stochastic electricity market model optimises the unit commitment considering four...... kinds of electricity markets (e.g. a spot and balancing market) and taking into account the stochastic behaviour of the wind power generation and of the prediction error. It can be used for the evaluation of varying electricity prices and system costs due to wind power integration...... and for the investigation of integration measures....
Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.
2017-01-01
We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.
Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.
2017-03-01
We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Cotter, Simon L.
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.
Nonlinear H{sub {infinity}} control of stochastic time-delay systems with Markovian switching
Energy Technology Data Exchange (ETDEWEB)
Wei Guoliang [School of Information Sciences and Technology, Donghua University, Shanghai 200051 (China); Wang Zidong [School of Information Sciences and Technology, Donghua University, Shanghai 200051 (China); Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH (United Kingdom)], E-mail: Zidong.Wang@brunel.ac.uk; Shu Huisheng [Department of Applied Mathematics, Donghua University, Shanghai 200051 (China)
2008-02-15
In this paper, the stabilization and H{sub {infinity}} control problems are investigated for a class of stochastic time-delay systems with both nonlinear disturbances and Markovian jumping parameters. The purpose of the stochastic stabilization problem is to design a memoryless state feedback controller such that, for the addressed nonlinear disturbances as well as Markovian jumping parameters, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. In the H{sub {infinity}} control problem, in addition to the mean-square exponential stability requirement, a prescribed H{sub {infinity}} performance index is required to be achieved. By using Ito's differential formula and the Lyapunov stability theory, sufficient conditions for the solvability of these problems are derived in term of linear matrix inequalities, which can be easily checked by resorting to available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed results.
Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems
Bashkirtseva, Irina; Ryashko, Lev
2016-04-01
A problem of stabilisation of the randomly forced periodic and quasiperiodic modes for nonlinear dynamic systems is considered. For this problem solution, we propose a new theoretical approach to consider these modes as invariant manifolds of the stochastic differential equations with control. The aim of the control is to provide the exponential mean square (EMS) stability for these manifolds. A general method of the stabilisation based on the algebraic criterion of the EMS-stability is elaborated. A constructive technique for the design of the feedback regulators stabilising various types of oscillatory regimes is proposed. A detailed parametric analysis of the problem of the stabilisation for stochastically forced periodic and quasiperiodic modes is given. An illustrative example of stochastic Hopf system is included to demonstrate the effectiveness of the proposed technique.
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.
Energy Technology Data Exchange (ETDEWEB)
Cai, Y.P.; Tan, Q. [Environmental Systems Engineering Program, Faculty of Engineering, Unversity of Regina, Regina, Saskatchewan (Canada); Huang, G.H. [Environmental Systems Engineering Program, Faculty of Engineering, Unversity of Regina, Regina, Saskatchewan (Canada)]|[Chinese Research Academy of Environmental Science, Beijing Normal University, Beijing 100012-100875 (China); Yang, Z.F. [State Key Laboratory of Water Environment Simulation, School of Enviroment, Beijing Normal University, Beijing 100875 (China)
2009-07-15
In this study, an interval-parameter superiority-inferiority-based two-stage programming model has been developed for supporting community-scale renewable energy management (ISITSP-CREM). This method is based on an integration of the existing interval linear programming (ILP), two-stage programming (TSP) and superiority-inferiority-based fuzzy-stochastic programming (SI-FSP). It allows uncertainties presented as both probability/possibilistic distributions and interval values to be incorporated within a general optimization framework, facilitating the reflection of multiple uncertainties and complexities during the process of renewable energy management systems planning. ISITSP-CREM can also be used for effectively addressing dynamic interrelationships between renewable energy availabilities, economic penalties and electricity-generation deficiencies within a community scale. Thus, complexities in renewable energy management systems can be systematically reflected, highly enhancing applicability of the modeling process. The developed method has then been applied to a case of long-term renewable energy management planning for three communities. Useful solutions for the planning of renewable energy management systems have been generated. Interval solutions associated with different energy availabilities and economic penalties have been obtained. They can be used for generating decision alternatives and thus help decision makers identify desired policies under various economic and system-reliability constraints. The generated solutions can also provide desired energy resource/service allocation plans with a minimized system cost (or economic penalties), a maximized system reliability level and a maximized energy security. Tradeoffs between system costs and energy security can also be tackled. Higher costs will increase potential energy generation amount, while a desire for lower system costs will run into a risk of energy deficiency. They are helpful for supporting
IDENTIFICATION OF BOTH CLOSED—AND OPEN—LOOP STOCHASTIC SYSTEM WHILE STABILIZING IT
Institute of Scientific and Technical Information of China (English)
CHENHanfu
2002-01-01
This paper proposes a recursive algorithm estimating coefficients of the linear stochastic control system(ARX system) driven by a martingale difference sequence,while adaptively stabilizing the system without introdudcing external excitation signal.The system is allowed to be unstable and of nonminimum-phase.The estimates derived for the coefficients of both closed-loop and open-loop systems are strongly consistent.
Kharchenko, D. O.
For the system with colored multiplicative noise the nonlinearity of the synergetic potential like φ^{2+m} model in Langevin equation was shown to be capable of providing the expanse of the stochastic system phase space. The concrete system of the population dynamics with the noise correlation time τ_cto∞ is examined. The fractal dimension of that kind of a system is defined as D=m, in contrast to the system with a white noise were D=0.
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
Directory of Open Access Journals (Sweden)
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.
Dimension reduction in stochastic analysis of coupled systems
Arnst, Maarten; Phipps, Eric; Red-Horse, John
2011-01-01
Coupled models with multiple physics, scales and/or domains arise in numerous areas of science and engineering. A key challenge in the formulation and implementation of coupled models is in facilitating the communication of information across physics, scale and/or domain interfaces. In a probabilistic context, any information that is communicated between model components is described in a statistical manner and requires an adapted probabilistic representation. While the number of sources of uncertainty can be expected to be large in many coupled problems, our contention is that exchanged statistical information often resides in a much lower dimensional space. In this work, we thus investigate the use of dimension-reduction techniques for the representation of exchanged information. We describe an adaptation of the Karhunen-Loeve decomposition to represent information as it is passed from component to component in a stochastic coupled model. The range of validity of the proposed dimension reduction is demonstr...
Variance-Constrained Multiobjective Control and Filtering for Nonlinear Stochastic Systems: A Survey
Directory of Open Access Journals (Sweden)
Lifeng Ma
2013-01-01
Full Text Available The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H2/H∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out.
Lin, Hai; Shuai, J. W.
2010-04-01
A stochastic spatial model based on the Monte Carlo approach is developed to study the dynamics of human immunodeficiency virus (HIV) infection. We aim to propose a more detailed and realistic simulation frame by incorporating many important features of HIV dynamics, which include infections, replications and mutations of viruses, antigen recognitions, activations and proliferations of lymphocytes, and diffusions, encounters and interactions of virions and lymphocytes. Our model successfully reproduces the three-phase pattern observed in HIV infection, and the simulation results for the time distribution from infection to AIDS onset are also in good agreement with the clinical data. The interactions of viruses and the immune system in all the three phases are investigated. We assess the relative importance of various immune system components in the acute phase. The dynamics of how the two important factors, namely the viral diversity and the asymmetric battle between HIV and the immune system, result in AIDS are investigated in detail with the model.
Energy Technology Data Exchange (ETDEWEB)
Lin Hai [Department of Chemical Biology, Xiamen University, Xiamen 361005 (China); Shuai, J W, E-mail: jianweishuai@xmu.edu.c [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China)
2010-04-15
A stochastic spatial model based on the Monte Carlo approach is developed to study the dynamics of human immunodeficiency virus (HIV) infection. We aim to propose a more detailed and realistic simulation frame by incorporating many important features of HIV dynamics, which include infections, replications and mutations of viruses, antigen recognitions, activations and proliferations of lymphocytes, and diffusions, encounters and interactions of virions and lymphocytes. Our model successfully reproduces the three-phase pattern observed in HIV infection, and the simulation results for the time distribution from infection to AIDS onset are also in good agreement with the clinical data. The interactions of viruses and the immune system in all the three phases are investigated. We assess the relative importance of various immune system components in the acute phase. The dynamics of how the two important factors, namely the viral diversity and the asymmetric battle between HIV and the immune system, result in AIDS are investigated in detail with the model.
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.
Energy Technology Data Exchange (ETDEWEB)
Milligan, M.; Donohoo, P.; O' Malley, M.
2012-09-01
Wind and solar generators differ in their generation characteristics than conventional generators. The variable output and imperfect predictability of these generators face a stochastic approach to plan and operate the power system without fundamentally changing the operation and planning problems. This paper overviews stochastic modeling challenges in operations, generation planning, and transmission planning, with references to current industry and academic work. Different stochastic problem formulations, including approximations, are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Milligan, M.; Donohoo, P.; O' Malley, M.
2012-09-01
Wind and solar generators differ in their generation characteristics than conventional generators. The variable output and imperfect predictability of these generators face a stochastic approach to plan and operate the power system without fundamentally changing the operation and planning problems. This paper overviews stochastic modeling challenges in operations, generation planning, and transmission planning, with references to current industry and academic work. Different stochastic problem formulations, including approximations, are also discussed.
Institute of Scientific and Technical Information of China (English)
Jiang Shi-Qi; Hou Min-Jie; Jia Chun-Hua; He Ji-Rong; Gu Tian-Xiang
2009-01-01
This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed. Several potential applications of parameter-induced stochastic resonance are given in circuits.
Directory of Open Access Journals (Sweden)
Jha Sumit
2012-04-01
Full Text Available Abstract Stochastic Differential Equations (SDE are often used to model the stochastic dynamics of biological systems. Unfortunately, rare but biologically interesting behaviors (e.g., oncogenesis can be difficult to observe in stochastic models. Consequently, the analysis of behaviors of SDE models using numerical simulations can be challenging. We introduce a method for solving the following problem: given a SDE model and a high-level behavioral specification about the dynamics of the model, algorithmically decide whether the model satisfies the specification. While there are a number of techniques for addressing this problem for discrete-state stochastic models, the analysis of SDE and other continuous-state models has received less attention. Our proposed solution uses a combination of Bayesian sequential hypothesis testing, non-identically distributed samples, and Girsanov's theorem for change of measures to examine rare behaviors. We use our algorithm to analyze two SDE models of tumor dynamics. Our use of non-identically distributed samples sampling contributes to the state of the art in statistical verification and model checking of stochastic models by providing an effective means for exposing rare events in SDEs, while retaining the ability to compute bounds on the probability that those events occur.
Jha, Sumit Kumar; Langmead, Christopher James
2012-04-12
Stochastic Differential Equations (SDE) are often used to model the stochastic dynamics of biological systems. Unfortunately, rare but biologically interesting behaviors (e.g., oncogenesis) can be difficult to observe in stochastic models. Consequently, the analysis of behaviors of SDE models using numerical simulations can be challenging. We introduce a method for solving the following problem: given a SDE model and a high-level behavioral specification about the dynamics of the model, algorithmically decide whether the model satisfies the specification. While there are a number of techniques for addressing this problem for discrete-state stochastic models, the analysis of SDE and other continuous-state models has received less attention. Our proposed solution uses a combination of Bayesian sequential hypothesis testing, non-identically distributed samples, and Girsanov's theorem for change of measures to examine rare behaviors. We use our algorithm to analyze two SDE models of tumor dynamics. Our use of non-identically distributed samples sampling contributes to the state of the art in statistical verification and model checking of stochastic models by providing an effective means for exposing rare events in SDEs, while retaining the ability to compute bounds on the probability that those events occur.
Delay induced transitions in an asymmetry bistable system and stochastic resonance
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The delay Fokker-Planck equation is given for an asymmetry bistable system with correlated Gaussian white noises. The small delay approximation based on the probability density approach is used and the approximate stationary probability density function is obtained. The phenomenon of delay induced transitions is found. When a weak periodic signal is added, the phenomenon of stochastic resonance is investigated. Expression of the signal-to-noise ratio (SNR) is obtained by using the two-state theory. It is shown that the time delay can suppress or promote the stochastic resonance phenomenon.
Synchronization of Coupled Stochastic Systems Driven by α-Stable Lévy Noises
Directory of Open Access Journals (Sweden)
Anhui Gu
2013-01-01
Full Text Available The synchronization of the solutions to coupled stochastic systems of N-Marcus stochastic ordinary differential equations which are driven by α-stable Lévy noises is investigated (N∈ℕ,1<α<2. We obtain the synchronization between two solutions and among different components of solutions under certain dissipative conditions. The synchronous phenomena persist no matter how large the intensity of the environment noises. These results generalize the work of two Marcus canonical equations in X. M. Liu et al.' s (2010.
Kao, Yonggui; Wang, Changhong; Xie, Jing; Karimi, Hamid Reza
2016-08-01
This paper investigates the delay-dependent stability problem for neutral Markovian jump systems with generally unknown transition rates (GUTRs). In this neutral GUTR model, each transition rate is completely unknown or only its estimate value is known. Based on the study of expectations of the stochastic cross-terms containing the ? integral, a new stability criterion is derived in terms of linear matrix inequalities. In the mathematical derivation process, bounding stochastic cross-terms, model transformation and free-weighting matrix are not employed for less conservatism. Finally, an example is provided to demonstrate the effectiveness of the proposed results.
Design of Microwave Band Pass Filters for the Debuncher Stochastic Cooling System
Energy Technology Data Exchange (ETDEWEB)
Deibele, C.; /Fermilab
2001-01-01
The FIR filters designed for the debuncher stochastic cooling system needed improvement. Its bandwidth was too wide, its magnitude was not flat, its phase ripple was too great, and it was difficult to control the characteristics of the filter. A simple microwave technique was employed to have a short time delay, simple robust layout, and small board size. A significant savings was seen over the FIR technique and these filters were installed in the Antiproton Source Debuncher while the FIR filters were removed from the debuncher stochastic cooling entirely.
A damage spreading transition in a stochastic host-pathogen system
Fried, Yael; Ben-Zion, Yossi; Shnerb, Nadav M.
2013-11-01
One of the leading proposals for solving the biodiversity problem is the Janzen-Connell hypothesis, suggesting that the abundance of a species is limited by a host-specific exploiter. Motivated by this model, here we analyze a spatially explicit host-pathogen system, looking for coexistence conditions under stochastic dynamics. Above the standard extinction transition associated with the failure of the pathogen to invade, we report another, damage spreading transition, marking the point where macroscopic clusters of host individuals disappear. Beyond its practical significance, this transition is apparently a generic landmark along the axis of decreasing stochasticity, if the deterministic dynamics support cycles or quasicycles.
Stochastic Parameter Resonance of Road-Vehicle Systems and Related Bifurcation Problems
Wedig, Walter V.
The paper investigates stochastic dynamics of road-vehicle systems and related bifurcation problems. The ride on rough roads generates vertical car vibrations whose root-mean-squares are resonant for critical car speeds and vanish when the car velocity is increasing, infinitely. These investigations are extended to wheel suspensions with progressive spring characteristics. For weak but still positive damping, the car vibrations become unstable when the velocity reaches the parameter resonance near twice the critical speed bifurcating into stochastic chaos of larger non-stationary car vibrations.
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.
Parametric Sensitivity Analysis for Stochastic Molecular Systems using Information Theoretic Metrics
Tsourtis, Anastasios; Katsoulakis, Markos A; Harmandaris, Vagelis
2014-01-01
In this paper we extend the parametric sensitivity analysis (SA) methodology proposed in Ref. [Y. Pantazis and M. A. Katsoulakis, J. Chem. Phys. 138, 054115 (2013)] to continuous time and continuous space Markov processes represented by stochastic differential equations and, particularly, stochastic molecular dynamics as described by the Langevin equation. The utilized SA method is based on the computation of the information-theoretic (and thermodynamic) quantity of relative entropy rate (RER) and the associated Fisher information matrix (FIM) between path distributions. A major advantage of the pathwise SA method is that both RER and pathwise FIM depend only on averages of the force field therefore they are tractable and computable as ergodic averages from a single run of the molecular dynamics simulation both in equilibrium and in non-equilibrium steady state regimes. We validate the performance of the extended SA method to two different molecular stochastic systems, a standard Lennard-Jones fluid and an al...
Breuer, H P; Petruccione, F; Breuer, Heinz-Peter; Kappler, Bernd; Petruccione, Francesco
1997-01-01
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\\bf 68}, 580 (1992)]. By means of a stan...
Accelerated stochastic and hybrid methods for spatial simulations of reaction diffusion systems
Rossinelli, Diego; Bayati, Basil; Koumoutsakos, Petros
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial τ-Leaping ( Sτ-Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid τ-Leaping ( Hτ-Leaping), combining a deterministic diffusion approximation with a τ-Leaping acceleration of the stochastic reactions. The algorithms are validated by solving Fisher's equation and used to explore the role of the number of particles in pattern formation. The results indicate that the present algorithms have a nearly constant time complexity with respect to the number of events (reaction and diffusion), unlike the exact stochastic simulation algorithm which scales linearly.
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.
Optimal variational principle for backward stochastic control systems associated with Lévy processes
Institute of Scientific and Technical Information of China (English)
TANG MaoNing; ZHANG Qi
2012-01-01
The paper is concerned with optimal control of backward stochastic differential equation (BSDE)driven by Teugel's martingales and an independent multi-dimensional Brownian motion,where Teugel's martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see e.g.,Nualart and Schoutens' paper in 2000).We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques.As an application,the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (or backward linear-quadratic problem,or BLQ problem for short) is discussed and characterized by a stochastic Hamilton system.
An Efficient and Exact Stochastic Simulation Method to Analyze Rare Events in Biochemical Systems
Kuwahara, Hiroyuki; Mura, Ivan
2008-01-01
In robust biological systems, wide deviations from highly controlled normal behavior may be rare, yet they may result in catastrophic complications. While in silico analysis has gained an appreciation as a tool to offer insights into systems-level properties of biological systems, analysis of such rare events provides a particularly challenging computational problem. This paper proposes an efficient stochastic simulation method to analyze rare events in biochemical systems. Our new approach c...
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging method.First,a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time delay.Then,stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system,and after that the Lyapunov function of the averaged It? equation is taken as the optimal linear combination of the corresponding independent first integrals in involution.Finally,the stability of the system is determined by using the largest eigenvalue of the linearized system.Two examples are used to illustrate the proposed procedure and the effects of delayed time on the Lyapunov stability are discussed as well.
Vladimirov, Igor G
2012-01-01
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system observables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to a class of quasilinear quantum stochastic systems which retain algebraic closedness in the evolution of mixed moments of the observables. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments of any order are amenable to exact analysis, including the computation of their steady-state values. In particular, a generalized criterion is developed for quadratic stability of the quasilinear systems. The results of the paper are applicable to the generation of non-Gaussian quantum states with manageable moments and an optimal design of linear quantum controllers for quasilinear...
Passivity-based sliding mode control for a polytopic stochastic differential inclusion system.
Liu, Leipo; Fu, Zhumu; Song, Xiaona
2013-11-01
Passivity-based sliding mode control for a polytopic stochastic differential inclusion (PSDI) system is considered. A control law is designed such that the reachability of sliding motion is guaranteed. Moreover, sufficient conditions for mean square asymptotic stability and passivity of sliding mode dynamics are obtained by linear matrix inequalities (LMIs). Finally, two examples are given to illustrate the effectiveness of the proposed method.
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-08-01
In this paper, a novel fractional equivalent linearization (EL) approach is developed by incorporating a fractional derivative term into the classical linearization equation. Due to the introduction of the fractional derivative term, the accuracy of the new linearization is improved, illustrated by a Duffing oscillator that is subjected to a harmonic excitation. Furthermore, a new method for solving stochastic response of nonlinear SDOF system is developed by combining Karhunen-Loève (K-L) expansion and fractional EL. The method firstly decomposes the stochastic excitation in terms of a set of random variables and deterministic sub-excitations using K-L expansion, and then construct sub-fractional equivalent linear system according to each sub-excitation by fractional EL, the response of the original nonlinear system is finally approximated as the weighed summation of the deterministic response of each sub-system multiplied by the corresponding random variable. The random nature of the final response comes from the set of random variables that is obtained in K-L expansion. In this way, the stochastic response computation is converted to a set of deterministic response analysis problems. The effectiveness of the developed method is demonstrated by a Duffing oscillator that is subjected to stochastic excitation modeled by Winner process. The results are compared with the numerical method and Monte Carlo simulation (MCS).
Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay
Directory of Open Access Journals (Sweden)
Xichao Sun
2013-01-01
Full Text Available This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.
Directory of Open Access Journals (Sweden)
Krishnan Balachandran
2011-06-01
Full Text Available We establish sufficient conditions for controllability of neutral impulsive stochastic quasilinear integrodifferential systems with nonlocal conditions in Hilbert spaces. The results are obtained by using semigroup theory, evolution operator and a fixed point technique. An example is provided to illustrate the obtained results.
Prescribing Transient and Asymptotic Behaviour of LTI Systems with Stochastic Initial Conditions
Dresscher, Martijn; Jayawardhana, Bayu
2017-01-01
This paper considers two different control problems for deterministic systems with stochastic initial conditions where, in addition to the usual asymptotic behavior requirement, we are interested in the transient behavior of the state distribution evolution. For the first one, we study control desig
Deterministic and Stochastic Analysis of a Prey-Dependent Predator-Prey System
Maiti, Alakes; Samanta, G. P.
2005-01-01
This paper reports on studies of the deterministic and stochastic behaviours of a predator-prey system with prey-dependent response function. The first part of the paper deals with the deterministic analysis of uniform boundedness, permanence, stability and bifurcation. In the second part the reproductive and mortality factors of the prey and…
Detection of weak stochastic forces in a parametrically stabilized micro-optomechanical system
Pontin, A.; Bonaldi, M.; Borrielli, A.; Cataliotti, F.S.; Marino, F.; Prodi, G.A.; Serra, E.; Marin, F.
2014-01-01
Measuring a weak force is an important task for micromechanical systems, both when using devices as sensitive detectors and, particularly, in experiments of quantum mechanics. The optimal strategy for resolving a weak stochastic signal force on a huge background (typically given by thermal noise) is
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...
Optimal coupling of heat and electricity systems: A stochastic hierarchical approach
DEFF Research Database (Denmark)
Mitridati, Lesia Marie-Jeanne Mariane; Pinson, Pierre
2016-01-01
already exist due to the participation of CHPs in both markets. New market structures must be developed in order to exploit these synergies. Recognizing the above-mentioned challenges this paper proposes a stochastic hierarchical formulation of the heat economic dispatch problem in a system with high...
Weisheimer, Antje; Corti, Susanna; Palmer, Tim; Vitart, Frederic
2014-06-28
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
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.
Stochastic Simulations of Cellular Biological Processes
2007-06-01
model kinetics of a system of chemical reactions is to use a stochastic 2. Stochastic Simulation Algorithm approach in terms of the Chemical Master...number of processors and running time) for interactive disk spae ad, herfor, my ceat meory simulations. Therefore, in addition to running in an...management problems for simulations involving a large inteative mode, foNScan as o run in ’n number of long runs or for large reaction networks. interactive
Institute of Scientific and Technical Information of China (English)
潘子刚; 刘允刚; 施颂椒
2001-01-01
In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An example is included to illustrate the theoretical findings.
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=g dt+{-D∇ϕ dt+√{2D} dB(t)}, with ∇ṡg=0 and {⋯} respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution u(x)=e. We find an orthogonality ∇ϕṡg=0 as a hallmark of the system. Stochastic thermodynamics based on time reversal (t,ϕ,g)→(-t,ϕ,-g) is formulated: entropy production ep#(t)=-dF(t)/dt; generalized “heat” hd#(t)=-dU(t)/dt, U(t)=∫ϕ(x)u(x,t) dx being “internal energy”, and “free energy” F(t)=U(t)+∫u(x,t)ln u(x,t) dx never increases. Entropy follows {dS}/{dt}=ep#-hd#. 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.
On the Hamiltonian structure of large deviations in stochastic hybrid systems
Bressloff, Paul C.; Faugeras, Olivier
2017-03-01
We present a new derivation of the classical action underlying a large deviation principle (LDP) for a stochastic hybrid system, which couples a piecewise deterministic dynamical system in {{{R}}d} with a time-homogeneous Markov chain on some discrete space Γ . We assume that the Markov chain on Γ is ergodic, and that the discrete dynamics is much faster than the piecewise deterministic dynamics (separation of time-scales). Using the Perron–Frobenius theorem and the calculus-of-variations, we show that the resulting action Hamiltonian is given by the Perron eigenvalue of a | Γ | -dimensional linear equation. The corresponding linear operator depends on the transition rates of the Markov chain and the nonlinear functions of the piecewise deterministic system. We compare the Hamiltonian to one derived using WKB methods, and show that the latter is a reduction of the former. We also indicate how the analysis can be extended to a multi-scale stochastic process, in which the continuous dynamics is described by a piecewise stochastic differential equations (SDE). Finally, we illustrate the theory by considering applications to conductance-based models of membrane voltage fluctuations in the presence of stochastic ion channels.
Stochastic stability of linear time-delay system with Markovian jumping parameters
Directory of Open Access Journals (Sweden)
K. Benjelloun
1997-01-01
Full Text Available This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP. We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.
Institute of Scientific and Technical Information of China (English)
Xiaowu MU; Haijun LIU
2007-01-01
In this paper,a state feedback adaptive stabilization for a class of large-scale stochastic nonlinear systems is designed with Lyapunov and Backstepping method.In the systems there are uncertain terms,whose bounds are governed by a set of unknown parameters.The designed controllers would make the close-loop systems asymptotically stable and adaptive for the unknown parameters.As an application,a second order example is delivered to illustrate the approach.
Guaranteed cost control for uncertain stochastic fuzzy systems with time delay
Institute of Scientific and Technical Information of China (English)
ZHANG Huaguang; WANG Yingchun
2007-01-01
This paper studies a delay-dependent guaranteed cost control problem for a class of uncertain nonlinear stochastic systems with time delay represented by the Takagi-Sugeno (T-S) fuzzy model with uncertain parameters. The descriptor system method and Gu's inequality are employed to obtain delay-dependent sufficient conditions such that the closed-loop system is asymptotically stable with a certain guaranteed cost control performance. The effectiveness of the proposed method is shown by a simulation example.
Institute of Scientific and Technical Information of China (English)
MA Song-Hua; LI Jing-Hui; JIANG Yong-Qing; FANG Jian-Ping
2008-01-01
A single (independent of each other) protein motor system with fluctuating potential barrier and subject to sine electric field is investigated. We first derive the approximate Langevin equation of this system with fluctuating potential barrier. Then from this approximate Langevin equation, we calculate the signal-to-noise ratio (SNR) in the adiabatic limit. The phenomenon of stochastic resonance is found for this protein motor system with fluctuating potential barrier.
CUMULANTS OF STOCHASTIC RESPONSE FOR A CLASS OF SPECIAL NONHOLONOMIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
SHANG MEI; ZHANG YI
2001-01-01
This paper studies the response cumulants for a kind of special nonholonomic systems under non-Gaussian, delta- correlated excitations. We present a new methodology for formulating the equations governing the evolution of the response cumulants of the stochastic dynamic systems. The response cumulant differential equations (CDEs) derived can be used to calculate the response cumulants for both linear and nonlinear systems. One example is given to illustrate how to use the CDEs for calculating response cumulants.
Stochastic Convection Parameterizations
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
Interactive Dynamic-System Simulation
Korn, Granino A
2010-01-01
Showing you how to use personal computers for modeling and simulation, Interactive Dynamic-System Simulation, Second Edition provides a practical tutorial on interactive dynamic-system modeling and simulation. It discusses how to effectively simulate dynamical systems, such as aerospace vehicles, power plants, chemical processes, control systems, and physiological systems. Written by a pioneer in simulation, the book introduces dynamic-system models and explains how software for solving differential equations works. After demonstrating real simulation programs with simple examples, the author
The interaction of seasonality and low-frequencies in a stochastic Arctic sea ice model
Moon, Woosok
2016-01-01
The stochastic Arctic sea ice model described as a single periodic non-autonomous stochastic ordinary differential equation (ODE) is useful in explaining the seasonal variability of Arctic sea ice. However, to be nearer to realistic approximations we consider the inclusion of long-term forcing implying the effect of slowly-varying ocean or atmospheric low-frequencies. In this research, we rely on the equivalent Fokker-Planck equation instead of the stochastic ODE owing to the advantages of the Fokker-Planck equation in dealing with higher moments calculations. We include simple long-term forcing into the Fokker-Planck equation and then seek approximate stochastic solutions. The formalism based on the Fokker-Planck equation with a singular perturbation method is flexible with regard to accommodating further complexity that arises due to the inclusion of long-term forcing. These solutions are then applied to the stochastic Arctic sea ice model with long-term forcing. Strong seasonality in the Arctic sea ice mod...
Number-Phase Wigner Representation for Scalable Stochastic Simulations of Controlled Quantum Systems
Hush, M R; Hope, J J
2011-01-01
Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as BEC and atom lasers, full quantum field simulations must rely on scalable stochastic methods whose convergence time is restricted by the use of representations based on coherent states. Here we show that typical measurements on atom-optical systems have a common form that allows for an efficient simulation using the number-phase Wigner (NPW) phase-space representation. We demonstrate that a stochastic method based on the NPW can converge over an order of magnitude longer and more precisely than its coherent equivalent. This opens the possibility of realistic simulations of controlled multi-mode quantum systems.