Chaos for Discrete Dynamical System
Directory of Open Access Journals (Sweden)
Lidong Wang
2013-01-01
Full Text Available We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.
Attractors for discrete periodic dynamical systems
John E. Franke; James F. Selgrade
2003-01-01
A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
Non-Lipschitz Dynamics Approach to Discrete Event Systems
Zak, M.; Meyers, R.
1995-01-01
This paper presents and discusses a mathematical formalism for simulation of discrete event dynamics (DED) - a special type of 'man- made' system designed to aid specific areas of information processing. A main objective is to demonstrate that the mathematical formalism for DED can be based upon the terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.
Geometric methods for discrete dynamical systems
Easton, Robert W
1998-01-01
This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley''s ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.
Essential uncontrollability of discrete linear, time-invariant, dynamical systems
Cliff, E. M.
1975-01-01
The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.
Design of Experiment Using Simulation of a Discrete Dynamical System
Directory of Open Access Journals (Sweden)
Mašek Jan
2016-12-01
Full Text Available The topic of the presented paper is a promising approach to achieve optimal Design of Experiment (DoE, i.e. spreading of points within a design domain, using a simulation of a discrete dynamical system of interacting particles within an n-dimensional design space. The system of mutually repelling particles represents a physical analogy of the Audze-Eglājs (AE optimization criterion and its periodical modification (PAE, respectively. The paper compares the performance of two approaches to implementation: a single-thread process using the JAVA language environment and a massively parallel solution employing the nVidia CUDA platform.
Directory of Open Access Journals (Sweden)
SERGIY KOZERENKO
2016-04-01
Full Text Available One feature of the famous Sharkovsky’s theorem is that it can be proved using digraphs of a special type (the so–called Markov graphs. The most general definition assigns a Markov graph to every continuous map from the topological graph to itself. We show that this definition is too broad, i.e. every finite digraph can be viewed as a Markov graph of some one–dimensional dynamical system on a tree. We therefore consider discrete analogues of Markov graphs for vertex maps on combinatorial trees and characterize all maps on trees whose discrete Markov graphs are of the following types: complete, complete bipartite, the disjoint union of cycles, with every arc being a loop.
Formal methods for discrete-time dynamical systems
Belta, Calin; Aydin Gol, Ebru
2017-01-01
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Modeling energy market dynamics using discrete event system simulation
International Nuclear Information System (INIS)
Gutierrez-Alcaraz, G.; Sheble, G.B.
2009-01-01
This paper proposes the use of Discrete Event System Simulation to study the interactions among fuel and electricity markets and consumers, and the decision-making processes of fuel companies (FUELCOs), generation companies (GENCOs), and consumers in a simple artificial energy market. In reality, since markets can reach a stable equilibrium or fail, it is important to observe how they behave in a dynamic framework. We consider a Nash-Cournot model in which marketers are depicted as Nash-Cournot players that determine supply to meet end-use consumption. Detailed engineering considerations such as transportation network flows are omitted, because the focus is upon the selection and use of appropriate market models to provide answers to policy questions. (author)
Modelling machine ensembles with discrete event dynamical system theory
Hunter, Dan
1990-01-01
Discrete Event Dynamical System (DEDS) theory can be utilized as a control strategy for future complex machine ensembles that will be required for in-space construction. The control strategy involves orchestrating a set of interactive submachines to perform a set of tasks for a given set of constraints such as minimum time, minimum energy, or maximum machine utilization. Machine ensembles can be hierarchically modeled as a global model that combines the operations of the individual submachines. These submachines are represented in the global model as local models. Local models, from the perspective of DEDS theory , are described by the following: a set of system and transition states, an event alphabet that portrays actions that takes a submachine from one state to another, an initial system state, a partial function that maps the current state and event alphabet to the next state, and the time required for the event to occur. Each submachine in the machine ensemble is presented by a unique local model. The global model combines the local models such that the local models can operate in parallel under the additional logistic and physical constraints due to submachine interactions. The global model is constructed from the states, events, event functions, and timing requirements of the local models. Supervisory control can be implemented in the global model by various methods such as task scheduling (open-loop control) or implementing a feedback DEDS controller (closed-loop control).
Integrated information in discrete dynamical systems: motivation and theoretical framework.
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David Balduzzi
2008-06-01
Full Text Available This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks
Integrated information in discrete dynamical systems: motivation and theoretical framework.
Balduzzi, David; Tononi, Giulio
2008-06-13
This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv) In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks are optimized
Positive dynamical systems in discrete time theory, models, and applications
Krause, Ulrich
2015-01-01
This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a systemare nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences.
Directory of Open Access Journals (Sweden)
Baogui Xin
2015-04-01
Full Text Available A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
Discrete Dynamical Systems Meet the Classic Monkey-and-the-Bananas Problem.
Gannon, Gerald E.; Martelli, Mario U.
2001-01-01
Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)
Discrete dynamics versus analytic dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2014-01-01
For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2017-07-01
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Discrete event dynamic system (DES)-based modeling for dynamic material flow in the pyroprocess
International Nuclear Information System (INIS)
Lee, Hyo Jik; Kim, Kiho; Kim, Ho Dong; Lee, Han Soo
2011-01-01
A modeling and simulation methodology was proposed in order to implement the dynamic material flow of the pyroprocess. Since the static mass balance provides the limited information on the material flow, it is hard to predict dynamic behavior according to event. Therefore, a discrete event system (DES)-based model named, PyroFlow, was developed at the Korea Atomic Energy Research Institute (KAERI). PyroFlow is able to calculate dynamic mass balance and also show various dynamic operational results in real time. By using PyroFlow, it is easy to rapidly predict unforeseeable results, such as throughput in unit process, accumulated product in buffer and operation status. As preliminary simulations, bottleneck analyses in the pyroprocess were carried out and consequently it was presented that operation strategy had influence on the productivity of the pyroprocess.
Directory of Open Access Journals (Sweden)
Chellaboina Vijaysekhar
2005-01-01
Full Text Available We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.
International Nuclear Information System (INIS)
Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.
2010-12-01
A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)
Estimation of system parameters in discrete dynamical systems from time series
International Nuclear Information System (INIS)
Palaniyandi, P.; Lakshmanan, M.
2005-01-01
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it needs a minimal number of time series data (either vector or scalar) and is applicable to dynamical systems of any dimension. The method also works extremely well even in the presence of noise in the time series. The method is specifically illustrated by means of logistic and Henon maps
GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems.
Elmeligy Abdelhamid, Sherif H; Kuhlman, Chris J; Marathe, Madhav V; Mortveit, Henning S; Ravi, S S
2015-01-01
Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.
International Nuclear Information System (INIS)
Zhao Gang-Ling; Chen Li-Qun; Fu Jing-Li; Hong Fang-Yu
2013-01-01
In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for the application of the results
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Winkel, Brian
2012-01-01
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)
Directory of Open Access Journals (Sweden)
L. Brim
2011-09-01
Full Text Available In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect the imposed level of approximation provided that with increasing parameter value the approximation converges to the original continuous system. By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems. The presented method and algorithms are evaluated on several exemplary biological models and on a real case study.
Schutte, Anne R; Spencer, John P
2007-04-01
The timed-initiation paradigm developed by Ghez and colleagues (1997) has revealed two modes of motor planning: continuous and discrete. Continuous responding occurs when targets are separated by less than 60 degrees of spatial angle, and discrete responding occurs when targets are separated by greater than 60 degrees . Although these two modes are thought to reflect the operation of separable strategic planning systems, a new theory of movement preparation, the Dynamic Field Theory, suggests that two modes emerge flexibly from the same system. Experiment 1 replicated continuous and discrete performance using a task modified to allow for a critical test of the single system view. In Experiment 2, participants were allowed to correct their movements following movement initiation (the standard task does not allow corrections). Results showed continuous planning performance at large and small target separations. These results are consistent with the proposal that the two modes reflect the time-dependent "preshaping" of a single planning system.
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
Asymptotic behavior of dynamical and control systems under perturbation and discretization
Grüne, Lars
2002-01-01
This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.
Bifurcation and complex dynamics of a discrete-time predator-prey system
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-06-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-I type in the closed first quadrant R+2. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. It has been found that the dynamical behavior of the model is very sensitive to the parameter values and the initial conditions. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamic behaviors, including phase portraits, period-9, 10, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2016-10-15
A new class of bifurcations is defined in discrete dynamical systems, and methods for their diagnostics and the analysis of their properties are presented. The TQ-bifurcations considered are implemented in discrete mappings and are related to the qualitative rearrangement of the shape of trajectories in an extended space of states. Within the demonstration of the main capabilities of the toolkit, an analysis is carried out of a logistic mapping in a domain to the right of the period-doubling limit point. Five critical values of the parameter are found for which the geometric structure of the trajectories of the mapping experiences a qualitative rearrangement. In addition, an analysis is carried out of the so-called “trace map,” which arises in the problems of quantum-mechanical description of various properties of discrete crystalline and quasicrystalline lattices.
Directory of Open Access Journals (Sweden)
V. Gontar
1997-01-01
Full Text Available A new theoretical foundation for the discrete dynamics of physicochemical systems is presented. Based on the analogy between the π-theorem of the theory of dimensionality, the second law of thermodynamics and the stoichiometry of complex physicochemical reactions, basic dynamic equations and an extreme principle were formulated. The meaning of discrete time and space in the proposed equations is discussed. Some results of numerical calculations are presented to demonstrate the potential of the proposed approach to the mathematical simulation of spatiotemporal physicochemical reaction dynamics.
General method to find the attractors of discrete dynamic models of biological systems
Gan, Xiao; Albert, Réka
2018-04-01
Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.
General method to find the attractors of discrete dynamic models of biological systems.
Gan, Xiao; Albert, Réka
2018-04-01
Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.
Geraci, Joseph; Dharsee, Moyez; Nuin, Paulo; Haslehurst, Alexandria; Koti, Madhuri; Feilotter, Harriet E; Evans, Ken
2014-03-01
We introduce a novel method for visualizing high dimensional data via a discrete dynamical system. This method provides a 2D representation of the relationship between subjects according to a set of variables without geometric projections, transformed axes or principal components. The algorithm exploits a memory-type mechanism inherent in a certain class of discrete dynamical systems collectively referred to as the chaos game that are closely related to iterative function systems. The goal of the algorithm was to create a human readable representation of high dimensional patient data that was capable of detecting unrevealed subclusters of patients from within anticipated classifications. This provides a mechanism to further pursue a more personalized exploration of pathology when used with medical data. For clustering and classification protocols, the dynamical system portion of the algorithm is designed to come after some feature selection filter and before some model evaluation (e.g. clustering accuracy) protocol. In the version given here, a univariate features selection step is performed (in practice more complex feature selection methods are used), a discrete dynamical system is driven by this reduced set of variables (which results in a set of 2D cluster models), these models are evaluated for their accuracy (according to a user-defined binary classification) and finally a visual representation of the top classification models are returned. Thus, in addition to the visualization component, this methodology can be used for both supervised and unsupervised machine learning as the top performing models are returned in the protocol we describe here. Butterfly, the algorithm we introduce and provide working code for, uses a discrete dynamical system to classify high dimensional data and provide a 2D representation of the relationship between subjects. We report results on three datasets (two in the article; one in the appendix) including a public lung cancer
Zeigler, Bernard P.
1989-01-01
It is shown how systems can be advantageously represented as discrete-event models by using DEVS (discrete-event system specification), a set-theoretic formalism. Such DEVS models provide a basis for the design of event-based logic control. In this control paradigm, the controller expects to receive confirming sensor responses to its control commands within definite time windows determined by its DEVS model of the system under control. The event-based contral paradigm is applied in advanced robotic and intelligent automation, showing how classical process control can be readily interfaced with rule-based symbolic reasoning systems.
Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.
Salceanu, Paul L
2011-07-01
This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of R(m+) to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.
Individual chaos implies collective chaos for weakly mixing discrete dynamical systems
International Nuclear Information System (INIS)
Liao Gongfu; Ma Xianfeng; Wang Lidong
2007-01-01
Let X be a metric space (X,f) a discrete dynamical system, where f:X->X is a continuous function. Let f-bar denote the natural extension of f to the space of all non-empty compact subsets of X endowed with Hausdorff metric induced by d. In this paper we investigate some dynamical properties of f and f-bar . It is proved that f is weakly mixing (mixing) if and only if f-bar is weakly mixing (mixing, respectively). From this, we deduce that weak-mixing of f implies transitivity of f-bar , further, if f is mixing or weakly mixing, then chaoticity of f (individual chaos) implies chaoticity of f-bar (collective chaos) and if X is a closed interval then f-bar is chaotic (in the sense of Devaney) if and only if f is weakly mixing
Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems.
Aftab, Muhammad Saleheen; Shafiq, Muhammad
2015-11-01
This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operating as controller and estimator. A Lyapunov function based back propagation learning algorithm is used for online adjustment of the controller and estimator parameters. The controller and estimator error convergence and closed-loop system stability analysis is performed by Lyapunov stability theory. Moreover, two simulation examples and one real-time experiment are investigated as case studies. The achieved results successfully validate the controller performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
A Discrete Dynamical System Approach to Pathway Activation Profiles of Signaling Cascades.
Catozzi, S; Sepulchre, J-A
2017-08-01
In living organisms, cascades of covalent modification cycles are one of the major intracellular signaling mechanisms, allowing to transduce physical or chemical stimuli of the external world into variations of activated biochemical species within the cell. In this paper, we develop a novel method to study the stimulus-response of signaling cascades and overall the concept of pathway activation profile which is, for a given stimulus, the sequence of activated proteins at each tier of the cascade. Our approach is based on a correspondence that we establish between the stationary states of a cascade and pieces of orbits of a 2D discrete dynamical system. The study of its possible phase portraits in function of the biochemical parameters, and in particular of the contraction/expansion properties around the fixed points of this discrete map, as well as their bifurcations, yields a classification of the cascade tiers into three main types, whose biological impact within a signaling network is examined. In particular, our approach enables to discuss quantitatively the notion of cascade amplification/attenuation from this new perspective. The method allows also to study the interplay between forward and "retroactive" signaling, i.e., the upstream influence of an inhibiting drug bound to the last tier of the cascade.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Directory of Open Access Journals (Sweden)
Yong Min
2013-06-01
Full Text Available In this paper, concepts and methods of hybrid control systems are adopted to establish a hierarchical dynamic automatic voltage control (HD-AVC system, realizing the dynamic voltage stability of power grids. An HD-AVC system model consisting of three layers is built based on the hybrid control method and discrete event-driven mechanism. In the Top Layer, discrete events are designed to drive the corresponding control block so as to avoid solving complex multiple objective functions, the power system’s characteristic matrix is formed and the minimum amplitude eigenvalue (MAE is calculated through linearized differential-algebraic equations. MAE is applied to judge the system’s voltage stability and security and construct discrete events. The Middle Layer is responsible for management and operation, which is also driven by discrete events. Control values of the control buses are calculated based on the characteristics of power systems and the sensitivity method. Then control values generate control strategies through the interface block. In the Bottom Layer, various control devices receive and implement the control commands from the Middle Layer. In this way, a closed-loop power system voltage control is achieved. Computer simulations verify the validity and accuracy of the HD-AVC system, and verify that the proposed HD-AVC system is more effective than normal voltage control methods.
Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.
Wei, Qinglai; Liu, Derong; Lin, Hanquan
2016-03-01
In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
The discrete adjoint method for parameter identification in multibody system dynamics.
Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin
2018-01-01
The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.
Autonomous learning by simple dynamical systems with a discrete-time formulation
Bilen, Agustín M.; Kaluza, Pablo
2017-05-01
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.
Energy Technology Data Exchange (ETDEWEB)
Shorikov, A. F. [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia and Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)
2014-11-18
We consider a discrete-time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector linear or convex discrete-time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solution.
International Nuclear Information System (INIS)
Leyendecker, Sigrid; Betsch, Peter; Steinmann, Paul
2008-01-01
In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367-391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy-momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method
Indian Academy of Sciences (India)
We also describe discrete-time systems in terms of difference ... A more modern alternative, especially for larger systems, is to convert ... In other words, ..... picture?) State-variable equations are also called state-space equations because the ...
Memorized discrete systems and time-delay
Luo, Albert C J
2017-01-01
This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling
Hesan, R.; Ghorbani, A.; Dignum, M.V.
2014-01-01
In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we
Sivak, David A; Chodera, John D; Crooks, Gavin E
2014-06-19
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.
Discrete dynamic modeling of cellular signaling networks.
Albert, Réka; Wang, Rui-Sheng
2009-01-01
Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
International Nuclear Information System (INIS)
Maslennikov, Oleg V.; Nekorkin, Vladimir I.
2016-01-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
A scheme for designing extreme multistable discrete dynamical ...
Indian Academy of Sciences (India)
A scheme for designing extreme multistable discrete dynamical systems ... Abstract. In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence ... Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700 009, India ...
Duality for discrete integrable systems
International Nuclear Information System (INIS)
Quispel, G R W; Capel, H W; Roberts, J A G
2005-01-01
A new class of discrete dynamical systems is introduced via a duality relation for discrete dynamical systems with a number of explicitly known integrals. The dual equation can be defined via the difference of an arbitrary linear combination of integrals and its upshifted version. We give an example of an integrable mapping with two parameters and four integrals leading to a (four-dimensional) dual mapping with four parameters and two integrals. We also consider a more general class of higher-dimensional mappings arising via a travelling-wave reduction from the (integrable) MKdV partial-difference equation. By differencing the trace of the monodromy matrix we obtain a class of novel dual mappings which is shown to be integrable as level-set-dependent versions of the original ones
Kouramas, K.I.; Faí sca, N.P.; Panos, C.; Pistikopoulos, E.N.
2011-01-01
This work presents a new algorithm for solving the explicit/multi- parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques
Noise Induced Dissipation in Discrete-Time Classical and Quantum Dynamical Systems
Wolowski, Lech
2004-01-01
We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed at which an initially closed, conservative system converges to the equilibrium when subjected to noisy (stochastic) perturbations. We prove fast dissipation result for classical Anosov systems and ...
International Nuclear Information System (INIS)
Li, Chunlong; Zhou, Jianzhong; Ouyang, Shuo; Ding, Xiaoling; Chen, Lu
2014-01-01
Highlights: • Optimization of large-scale hydropower system in the Yangtze River basin. • Improved decomposition–coordination and discrete differential dynamic programming. • Generating initial solution randomly to reduce generation time. • Proposing relative coefficient for more power generation. • Proposing adaptive bias corridor technology to enhance convergence speed. - Abstract: With the construction of major hydro plants, more and more large-scale hydropower systems are taking shape gradually, which brings up a challenge to optimize these systems. Optimization of large-scale hydropower system (OLHS), which is to determine water discharges or water levels of overall hydro plants for maximizing total power generation when subjecting to lots of constrains, is a high dimensional, nonlinear and coupling complex problem. In order to solve the OLHS problem effectively, an improved decomposition–coordination and discrete differential dynamic programming (IDC–DDDP) method is proposed in this paper. A strategy that initial solution is generated randomly is adopted to reduce generation time. Meanwhile, a relative coefficient based on maximum output capacity is proposed for more power generation. Moreover, an adaptive bias corridor technology is proposed to enhance convergence speed. The proposed method is applied to long-term optimal dispatches of large-scale hydropower system (LHS) in the Yangtze River basin. Compared to other methods, IDC–DDDP has competitive performances in not only total power generation but also convergence speed, which provides a new method to solve the OLHS problem
Discrete port-Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2006-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system
Energy Technology Data Exchange (ETDEWEB)
Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)
2015-11-30
We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.
Two new discrete integrable systems
International Nuclear Information System (INIS)
Chen Xiao-Hong; Zhang Hong-Qing
2013-01-01
In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Ã 1 . By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity
Trivial dynamics in discrete-time systems: carrying simplex and translation arcs
Niu, Lei; Ruiz-Herrera, Alfonso
2018-06-01
In this paper we show that the dynamical behavior in (first octant) of the classical Kolmogorov systems of competitive type admitting a carrying simplex can be sometimes determined completely by the number of fixed points on the boundary and the local behavior around them. Roughly speaking, T has trivial dynamics (i.e. the omega limit set of any orbit is a connected set contained in the set of fixed points) provided T has exactly four hyperbolic nontrivial fixed points in with local attractors on the carrying simplex and local repellers on the carrying simplex; and there exists a unique hyperbolic fixed point in Int. Our results are applied to some classical models including the Leslie–Gower models, Atkinson-Allen systems and Ricker maps.
Ensemble simulations with discrete classical dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2013-01-01
For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\\tilde{H}$ with energy $\\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\\tilde{H}$. $\\tilde......{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics...
Directory of Open Access Journals (Sweden)
D. A. Eliseev
2015-01-01
Full Text Available The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.
Causal Dynamics of Discrete Surfaces
Directory of Open Access Journals (Sweden)
Pablo Arrighi
2014-03-01
Full Text Available We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
Can time be a discrete dynamical variable
International Nuclear Information System (INIS)
Lee, T.D.
1983-01-01
The possibility that time can be regarded as a discrete dynamical variable is examined through all phases of mechanics: from classical mechanics to nonrelativistic quantum mechanics, and to relativistic quantum field theories. (orig.)
McDonough, J M
2009-06-01
Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the "poor man's Navier-Stokes equation." Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.
Discretization model for nonlinear dynamic analysis of three dimensional structures
International Nuclear Information System (INIS)
Hayashi, Y.
1982-12-01
A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt
Fayolle, G; Fayolle, Guy; Furtlehner, Cyril
2006-01-01
This report is the foreword of a series of stochastic deformations of curves. Problems are set in terms of exclusion processes, the ultimate goal being to derive hydrodynamic limits for these systems after proper scalings. In this study, solely the basic texts system on the torus is analyzed. The usual sequence of empirical measures, converges in probability to a deterministic measure, which is the unique weak solution of a Cauchy problem. The method presents some new features, letting hope for extensions to higher dimension. It relies on the analysis of a family of parabolic differential operators, involving variational calculus. Namely, the variables are the values of functions at given points, their number being possibly infinite.
Supervisory Control Technique For An Assembly Workstation As A Dynamic Discrete Event System
Directory of Open Access Journals (Sweden)
Daniela Cristina CERNEGA
2001-12-01
Full Text Available This paper proposes a control problem statement in the framework of supervisory control technique for the assembly workstations. A desired behaviour of an assembly workstation is analysed. The behaviour of such a workstation is cyclic and some linguistic properties are established. In this paper, it is proposed an algorithm for the computation of the supremal controllable language of the closed system desired language. Copyright © 2001 IFAC.
Discrete dynamics in transitional economies
Directory of Open Access Journals (Sweden)
J. Barkley Rosser, Jr.
1998-01-01
Full Text Available This paper traces the transition from planned command socialism to market capitalism and the accompanying complex non-linear dynamics involved. Long wave chaotic hysteretic investment cycles emerge under socialism leading to crisis and breakdown. Macroeconomic collapse occurs with bifurcations of coordination structures during transition. During recovery, transitional cobweb labor market dynamics exhibit chaos, fractal basin boundaries between coexisting non-chaotic attractors, discontinuous phase transitions, strange attractors, and cascades of infinitely many period-doubling bifurcations.
A Discrete Dynamical Model of Signed Partitions
Directory of Open Access Journals (Sweden)
G. Chiaselotti
2013-01-01
Full Text Available We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.
A study of discrete nonlinear systems
International Nuclear Information System (INIS)
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
Discrete modeling considerations in multiphase fluid dynamics
International Nuclear Information System (INIS)
Ransom, V.H.; Ramshaw, J.D.
1988-01-01
The modeling of multiphase flows play a fundamental role in light water reactor safety. The main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must be cast into discrete form for a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is potentially hazardous. It may be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a statistical closure problem. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples. 48 refs
Discrete Control Processes, Dynamic Games and Multicriterion Control Problems
Directory of Open Access Journals (Sweden)
Dumitru Lozovanu
2002-07-01
Full Text Available The discrete control processes with state evaluation in time of dynamical system is considered. A general model of control problems with integral-time cost criterion by a trajectory is studied and a general scheme for solving such classes of problems is proposed. In addition the game-theoretical and multicriterion models for control problems are formulated and studied.
Kouramas, K.I.
2011-08-01
This work presents a new algorithm for solving the explicit/multi- parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step. © 2011 Elsevier Ltd. All rights reserved.
Switching dynamics in reaction networks induced by molecular discreteness
International Nuclear Information System (INIS)
Togashi, Yuichi; Kaneko, Kunihiko
2007-01-01
To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states
Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate
Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan
2011-01-01
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate
Directory of Open Access Journals (Sweden)
Huayong Zhang
2018-01-01
Full Text Available We present in this paper an investigation on a discrete predator-prey system with Crowley-Martin type functional response to know its complex dynamics on the routes to chaos which are induced by bifurcations. Via application of the center manifold theorem and bifurcation theorems, occurrence conditions for flip bifurcation and Neimark-Sacker bifurcation are determined, respectively. Numerical simulations are performed, on the one hand, verifying the theoretical results and, on the other hand, revealing new interesting dynamical behaviors of the discrete predator-prey system, including period-doubling cascades, period-2, period-3, period-4, period-5, period-6, period-7, period-8, period-9, period-11, period-13, period-15, period-16, period-20, period-22, period-24, period-30, and period-34 orbits, invariant cycles, chaotic attractors, sub-flip bifurcation, sub-(inverse Neimark-Sacker bifurcation, chaotic interior crisis, chaotic band, sudden disappearance of chaotic dynamics and abrupt emergence of chaos, and intermittent periodic behaviors. Moreover, three-dimensional bifurcation diagrams are utilized to study the transition between flip bifurcation and Neimark-Sacker bifurcation, and a critical case between the two bifurcations is found. This critical bifurcation case is a combination of flip bifurcation and Neimark-Sacker bifurcation, showing the nonlinear characteristics of both bifurcations.
Mizell, Carolyn Barrett; Malone, Linda
2007-01-01
The development process for a large software development project is very complex and dependent on many variables that are dynamic and interrelated. Factors such as size, productivity and defect injection rates will have substantial impact on the project in terms of cost and schedule. These factors can be affected by the intricacies of the process itself as well as human behavior because the process is very labor intensive. The complex nature of the development process can be investigated with software development process models that utilize discrete event simulation to analyze the effects of process changes. The organizational environment and its effects on the workforce can be analyzed with system dynamics that utilizes continuous simulation. Each has unique strengths and the benefits of both types can be exploited by combining a system dynamics model and a discrete event process model. This paper will demonstrate how the two types of models can be combined to investigate the impacts of human resource interactions on productivity and ultimately on cost and schedule.
Discrete port-Hamiltonian systems : mixed interconnections
Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der
2005-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Discrete-Time Nonlinear Control of VSC-HVDC System
Directory of Open Access Journals (Sweden)
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
Discrete modelling of drapery systems
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
Control of Discrete Event Systems
Smedinga, Rein
1989-01-01
Systemen met discrete gebeurtenissen spelen in vele gebieden een rol. In dit proefschrift staat de volgorde van gebeurtenissen centraal en worden tijdsaspecten buiten beschouwing gelaten. In dat geval kunnen systemen met discrete gebeurtenissen goed worden gemodelleerd door gebruik te maken van
Modelling and real-time simulation of continuous-discrete systems in mechatronics
Energy Technology Data Exchange (ETDEWEB)
Lindow, H. [Rostocker, Magdeburg (Germany)
1996-12-31
This work presents a methodology for simulation and modelling of systems with continuous - discrete dynamics. It derives hybrid discrete event models from Lagrange`s equations of motion. This method combines continuous mechanical, electrical and thermodynamical submodels on one hand with discrete event models an the other hand into a hybrid discrete event model. This straight forward software development avoids numeric overhead.
Indirect adaptive control of discrete chaotic systems
International Nuclear Information System (INIS)
Salarieh, Hassan; Shahrokhi, Mohammad
2007-01-01
In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations
Wang, Jun-Sheng; Yang, Guang-Hong
2017-07-25
This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.
Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.
1996-01-01
Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...
Charles, Alexandre; Ballard, Patrick
2016-08-01
The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this
Fermion systems in discrete space-time
International Nuclear Information System (INIS)
Finster, Felix
2007-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure
Fermion systems in discrete space-time
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)
2007-05-15
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion Systems in Discrete Space-Time
Finster, Felix
2006-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion systems in discrete space-time
Finster, Felix
2007-05-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
A dynamic discretization method for reliability inference in Dynamic Bayesian Networks
International Nuclear Information System (INIS)
Zhu, Jiandao; Collette, Matthew
2015-01-01
The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem. - Highlights: • A dynamic discretization method is developed for low-probability events in DBNs. • The method is compared to existing approaches on two crack growth problems. • The method is shown to improve on existing methods for low-probability events
Parallel Stochastic discrete event simulation of calcium dynamics in neuron.
Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W
2017-09-26
The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.
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.
Rich dynamics of discrete delay ecological models
International Nuclear Information System (INIS)
Peng Mingshu
2005-01-01
We study multiple bifurcations and chaotic behavior of a discrete delay ecological model. New form of chaos for the 2-D map is observed: the combination of potential period doubling and reverse period-doubling leads to cascading bubbles
Experiments of reconstructing discrete atmospheric dynamic models from data (I)
Lin, Zhenshan; Zhu, Yanyu; Deng, Ziwang
1995-03-01
In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, x n + 1 = 1- μx {2/n}, could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.
Comments on `A discrete optimal control problem for descriptor systems'
DEFF Research Database (Denmark)
Ravn, Hans
1990-01-01
In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates that there ......In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates...
Exact wave packet decoherence dynamics in a discrete spectrum environment
International Nuclear Information System (INIS)
Tu, Matisse W Y; Zhang Weimin
2008-01-01
We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet in an environment containing a few discrete modes. We obtain two intrinsic energy scales relating to the time scales of the system and the environment. The different relationship between these two scales alters the overall form of the solution of the system. We also introduce a decoherence measure for a single wave packet which is defined as the ratio of Schroedinger uncertainty over the delocalization extension of the wave packet and characterizes the time-evolution behaviour of the off-diagonal reduced density matrix element. We utilize the exact solution and the decoherence measure to study the wave packet decoherence dynamics. We further demonstrate how the dynamical diffusion of the wave packet leads to non-Markovian decoherence in such a microscopic environment.
Discrete dynamic modeling of T cell survival signaling networks
Zhang, Ranran
2009-03-01
Biochemistry-based frameworks are often not applicable for the modeling of heterogeneous regulatory systems that are sparsely documented in terms of quantitative information. As an alternative, qualitative models assuming a small set of discrete states are gaining acceptance. This talk will present a discrete dynamic model of the signaling network responsible for the survival and long-term competence of cytotoxic T cells in the blood cancer T-LGL leukemia. We integrated the signaling pathways involved in normal T cell activation and the known deregulations of survival signaling in leukemic T-LGL, and formulated the regulation of each network element as a Boolean (logic) rule. Our model suggests that the persistence of two signals is sufficient to reproduce all known deregulations in leukemic T-LGL. It also indicates the nodes whose inactivity is necessary and sufficient for the reversal of the T-LGL state. We have experimentally validated several model predictions, including: (i) Inhibiting PDGF signaling induces apoptosis in leukemic T-LGL. (ii) Sphingosine kinase 1 and NFκB are essential for the long-term survival of T cells in T-LGL leukemia. (iii) T box expressed in T cells (T-bet) is constitutively activated in the T-LGL state. The model has identified potential therapeutic targets for T-LGL leukemia and can be used for generating long-term competent CTL necessary for tumor and cancer vaccine development. The success of this model, and of other discrete dynamic models, suggests that the organization of signaling networks has an determining role in their dynamics. Reference: R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, T. P. Loughran, Jr., Network Model of Survival Signaling in LGL Leukemia, PNAS 105, 16308-16313 (2008).
Discretization-induced delays and their role in the dynamics
International Nuclear Information System (INIS)
Ramani, A; Grammaticos, B; Satsuma, J; Willox, R
2008-01-01
We show that a discretization of a continuous system may entail 'hidden' delays and thus introduce instabilities. In this case, while the continuous system has an attractive fixed point, the instabilities present in the equivalent discrete one may lead to the appearance of a limit cycle. We explain that it is possible, thanks to the proper staggering of the discrete variables, to eliminate the hidden delay. However, in general, other instabilities may appear in the discrete system which can even lead to chaotic behaviour
The discrete dynamics of symmetric competition in the plane.
Jiang, H; Rogers, T D
1987-01-01
We consider the generalized Lotka-Volterra two-species system xn + 1 = xn exp(r1(1 - xn) - s1yn) yn + 1 = yn exp(r2(1 - yn) - s2xn) originally proposed by R. M. May as a model for competitive interaction. In the symmetric case that r1 = r2 and s1 = s2, a region of ultimate confinement is found and the dynamics therein are described in some detail. The bifurcations of periodic points of low period are studied, and a cascade of period-doubling bifurcations is indicated. Within the confinement region, a parameter region is determined for the stable Hopf bifurcation of a pair of symmetrically placed period-two points, which imposes a second component of oscillation near the stable cycles. It is suggested that the symmetric competitive model contains much of the dynamical complexity to be expected in any discrete two-dimensional competitive model.
Nonlinear integrodifferential equations as discrete systems
Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.
1999-06-01
We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.
Discrete Model Reference Adaptive Control System for Automatic Profiling Machine
Directory of Open Access Journals (Sweden)
Peng Song
2012-01-01
Full Text Available Automatic profiling machine is a movement system that has a high degree of parameter variation and high frequency of transient process, and it requires an accurate control in time. In this paper, the discrete model reference adaptive control system of automatic profiling machine is discussed. Firstly, the model of automatic profiling machine is presented according to the parameters of DC motor. Then the design of the discrete model reference adaptive control is proposed, and the control rules are proven. The results of simulation show that adaptive control system has favorable dynamic performances.
Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
Cresson, Jacky; Pierret, Frédéric
2015-01-01
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.
Analysis hierarchical model for discrete event systems
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Multistability and complex dynamics in a simple discrete economic model
International Nuclear Information System (INIS)
Peng Mingshu; Jiang Zhonghao; Jiang Xiaoxia; Hu Jiping; Qu Youli
2009-01-01
In this paper, we will propose a generalized Cournot duopoly model with Z 2 symmetry. We demonstrate that cost functions incorporating an interfirm externality lead to a system of couple one-dimensional maps. In the situation where agents take turns, we find in an analytic way that there coexist multiple unstable/stable period-2 cycles or synchronized/asynchronized periodic orbits. Coupling one-dimension chaos can be observed. In a more general situation, where agents move simultaneously, a closer analysis reveals some well-known local bifurcations and global bifurcations which typically occur in two-parameter families of two-dimensional discrete time dynamical systems, including codimension-one (fold-, flip-, Neimark-Sacker-) bifurcations, codimension-two (fold/flip, 1:2 resonance, 1:3 resonance and 1:4 resonance) bifurcations, and hetero-clinic, homo-clinic bifurcations, etc. Multistability, including the coexistence of synchronized/asynchronized solutions are also discussed.
Modeling and simulation of discrete event systems
Choi, Byoung Kyu
2013-01-01
Computer modeling and simulation (M&S) allows engineers to study and analyze complex systems. Discrete-event system (DES)-M&S is used in modern management, industrial engineering, computer science, and the military. As computer speeds and memory capacity increase, so DES-M&S tools become more powerful and more widely used in solving real-life problems. Based on over 20 years of evolution within a classroom environment, as well as on decades-long experience in developing simulation-based solutions for high-tech industries, Modeling and Simulation of Discrete-Event Systems is the only book on
Exterior difference systems and invariance properties of discrete mechanics
International Nuclear Information System (INIS)
Xie Zheng; Xie Duanqiang; Li Hongbo
2008-01-01
Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms
International Nuclear Information System (INIS)
Kim, Do Hun; Mun, Tae Hun; Kim, Dong Hwan
1999-02-01
This book introduces systems thinking and conceptual tool and modeling tool of dynamics system such as tragedy of single thinking, accessible way of system dynamics, feedback structure and causal loop diagram analysis, basic of system dynamics modeling, causal loop diagram and system dynamics modeling, information delay modeling, discovery and application for policy, modeling of crisis of agricultural and stock breeding products, dynamic model and lesson in ecosystem, development and decadence of cites and innovation of education forward system thinking.
Dynamic generation of light states with discrete symmetries
Cordero, S.; Nahmad-Achar, E.; Castaños, O.; López-Peña, R.
2018-01-01
A dynamic procedure is established within the generalized Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group Cn. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of three-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, |ψ〉 M1,and |ψ〉 M 2, is considered. It can be generated by the proper selection of the time of flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order n =| M1-M2| .
Nonlinear wave propagation in discrete and continuous systems
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Discrete and continuous time dynamic mean-variance analysis
Reiss, Ariane
1999-01-01
Contrary to static mean-variance analysis, very few papers have dealt with dynamic mean-variance analysis. Here, the mean-variance efficient self-financing portfolio strategy is derived for n risky assets in discrete and continuous time. In the discrete setting, the resulting portfolio is mean-variance efficient in a dynamic sense. It is shown that the optimal strategy for n risky assets may be dominated if the expected terminal wealth is constrained to exactly attain a certain goal instead o...
Discrete time and continuous time dynamic mean-variance analysis
Reiss, Ariane
1999-01-01
Contrary to static mean-variance analysis, very few papers have dealt with dynamic mean-variance analysis. Here, the mean-variance efficient self-financing portfolio strategy is derived for n risky assets in discrete and continuous time. In the discrete setting, the resulting portfolio is mean-variance efficient in a dynamic sense. It is shown that the optimal strategy for n risky assets may be dominated if the expected terminal wealth is constrained to exactly attain a certain goal instead o...
Discrete time population dynamics of a two-stage species with recruitment and capture
International Nuclear Information System (INIS)
Ladino, Lilia M.; Mammana, Cristiana; Michetti, Elisabetta; Valverde, Jose C.
2016-01-01
This work models and analyzes the dynamics of a two-stage species with recruitment and capture factors. It arises from the discretization of a previous model developed by Ladino and Valverde (2013), which represents a progress in the knowledge of the dynamics of exploited populations. Although the methods used here are related to the study of discrete-time systems and are different from those related to continuous version, the results are similar in both the discrete and the continuous case what confirm the skill in the selection of the factors to design the model. Unlike for the continuous-time case, for the discrete-time one some (non-negative) parametric constraints are derived from the biological significance of the model and become fundamental for the proofs of such results. Finally, numerical simulations show different scenarios of dynamics related to the analytical results which confirm the validity of the model.
Discrete integrable systems and deformations of associative algebras
International Nuclear Information System (INIS)
Konopelchenko, B G
2009-01-01
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.
International Nuclear Information System (INIS)
Huo Haifeng; Li Wantong
2009-01-01
This paper is concerned with the global stability characteristics of a system of equations modelling the dynamics of continuous-time bidirectional associative memory neural networks with impulses. Sufficient conditions which guarantee the existence of a unique equilibrium and its exponential stability of the networks are obtained. For the goal of computation, discrete-time analogues of the corresponding continuous-time bidirectional associative memory neural networks with impulses are also formulated and studied. Our results show that the above continuous-time and discrete-time systems with impulses preserve the dynamics of the networks without impulses when we make some modifications and impose some additional conditions on the systems, the convergence characteristics dynamics of the networks are preserved by both continuous-time and discrete-time systems with some restriction imposed on the impulse effect.
Noether symmetries of discrete mechanico–electrical systems
International Nuclear Information System (INIS)
Fu Jingli; Xie Fengping; Chen Benyong
2008-01-01
This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)
Generalized Detectability for Discrete Event Systems
Shu, Shaolong; Lin, Feng
2011-01-01
In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems. PMID:21691432
Constant pressure and temperature discrete-time Langevin molecular dynamics
Energy Technology Data Exchange (ETDEWEB)
Grønbech-Jensen, Niels [Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States); Department of Mathematics, University of California, Davis, California 95616 (United States); Farago, Oded [Department of Biomedical Engineering, Ben Gurion University of the Negev, Be' er Sheva 84105 (Israel); Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Be' er Sheva 84105 (Israel)
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Fractal sets generated by chemical reactions discrete chaotic dynamics
International Nuclear Information System (INIS)
Gontar, V.; Grechko, O.
2007-01-01
Fractal sets composed by the parameters values of difference equations derived from chemical reactions discrete chaotic dynamics (DCD) and corresponding to the sequences of symmetrical patterns were obtained in this work. Examples of fractal sets with the corresponding symmetrical patterns have been presented
Discrete-time control system design with applications
Rabbath, C A
2014-01-01
This book presents practical techniques of discrete-time control system design. In general, the design techniques lead to low-order dynamic compensators that ensure satisfactory closed-loop performance for a wide range of sampling rates. The theory is given in the form of theorems, lemmas, and propositions. The design of the control systems is presented as step-by-step procedures and algorithms. The proposed feedback control schemes are applied to well-known dynamic system models. This book also discusses: Closed-loop performance of generic models of mobile robot and airborne pursuer dynamic systems under discrete-time feedback control with limited computing capabilities Concepts of discrete-time models and sampled-data models of continuous-time systems, for both single- and dual-rate operation Local versus global digital redesign Optimal, closed-loop digital redesign methods Plant input mapping design Generalized holds and samplers for use in feedback control loops, Numerical simulation of fixed-point arithm...
Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot
Marcin Szuster; Zenon Hendzel
2014-01-01
Network-based control systems have been emerging technologies in the control of nonlinear systems over the past few years. This paper focuses on the implementation of the approximate dynamic programming algorithm in the network-based tracking control system of the two-wheeled mobile robot, Pioneer 2-DX. The proposed discrete tracking control system consists of the globalised dual heuristic dynamic programming algorithm, the PD controller, the supervisory term, and an additional control signal...
Quasicanonical structure of optimal control in constrained discrete systems
Sieniutycz, S.
2003-06-01
This paper considers discrete processes governed by difference rather than differential equations for the state transformation. The basic question asked is if and when Hamiltonian canonical structures are possible in optimal discrete systems. Considering constrained discrete control, general optimization algorithms are derived that constitute suitable theoretical and computational tools when evaluating extremum properties of constrained physical models. The mathematical basis of the general theory is the Bellman method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage criterion which allows a variation of the terminal state that is otherwise fixed in the Bellman's method. Two relatively unknown, powerful optimization algorithms are obtained: an unconventional discrete formalism of optimization based on a Hamiltonian for multistage systems with unconstrained intervals of holdup time, and the time interval constrained extension of the formalism. These results are general; namely, one arrives at: the discrete canonical Hamilton equations, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory along with all basic results of variational calculus. Vast spectrum of applications of the theory is briefly discussed.
Discrete Opinion Dynamics on Online Social Networks
Hu, Yan-Li; Bai, Liang; Zhang, Wei-Ming
2013-01-01
This paper focuses on the dynamics of binary opinions {+1, -1} on online social networks consisting of heterogeneous actors. In our model, actors update their opinions under the interplay of social influence and self- affirmation, which leads to rich dynamical behaviors on online social networks. We find that the opinion leading to the consensus features an advantage of the initially weighted fraction based on actors' strength over the other, instead of the population. For the role of specific actors, the consensus converges towards the opinion that a small fraction of high-strength actors hold, and individual diversity of self-affirmation slows down the ordering process of consensus. These indicate that high-strength actors play an essential role in opinion formation with strong social influence as well as high persistence. Further investigations show that the initial fraction of high-strength actors to dominate the evolution depends on the heterogeneity of the strength distribution, and less high-strength actors are needed in the case of a smaller exponent of power-law distribution of actors' strength. Our study provides deep insights into the role of social influence and self-affirmation on opinion formation on online social networks.
Discrete Opinion Dynamics on Online Social Networks
International Nuclear Information System (INIS)
Hu Yan-Li; Bai Liang; Zhang Wei-Ming
2013-01-01
This paper focuses on the dynamics of binary opinions {+1, −1} on online social networks consisting of heterogeneous actors. In our model, actors update their opinions under the interplay of social influence and self- affirmation, which leads to rich dynamical behaviors on online social networks. We find that the opinion leading to the consensus features an advantage of the initially weighted fraction based on actors' strength over the other, instead of the population. For the role of specific actors, the consensus converges towards the opinion that a small fraction of high-strength actors hold, and individual diversity of self-affirmation slows down the ordering process of consensus. These indicate that high-strength actors play an essential role in opinion formation with strong social influence as well as high persistence. Further investigations show that the initial fraction of high-strength actors to dominate the evolution depends on the heterogeneity of the strength distribution, and less high-strength actors are needed in the case of a smaller exponent of power-law distribution of actors' strength. Our study provides deep insights into the role of social influence and self-affirmation on opinion formation on online social networks. (general)
A 2+1 non-isospectral discrete integrable system and its discrete integrable coupling system
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2006-01-01
In this Letter by considering a (2+1)-dimensional discrete non-isospectral linear problem, a new (2+1)-dimensional integrable lattice hierarchy is constructed. It shows that generalization of the Blaszak-Marciniak lattice hierarchy can be obtained as a reduction. Then an extended algebraic system X-bar of X is presented, from which the integrable coupling system of the (2+1)-dimensional discrete non-isospectral Blaszak-Marciniak lattice equations are obtained
Discrete event systems diagnosis and diagnosability
Sayed-Mouchaweh, Moamar
2014-01-01
Discrete Event Systems: Diagnosis and Diagnosability addresses the problem of fault diagnosis of Discrete Event Systems (DES). This book provides the basic techniques and approaches necessary for the design of an efficient fault diagnosis system for a wide range of modern engineering applications. The different techniques and approaches are classified according to several criteria such as: modeling tools (Automata, Petri nets) that is used to construct the model; the information (qualitative based on events occurrences and/or states outputs, quantitative based on signal processing and data analysis) that is needed to analyze and achieve the diagnosis; the decision structure (centralized, decentralized) that is required to achieve the diagnosis. The goal of this classification is to select the efficient method to achieve the fault diagnosis according to the application constraints. This book focuses on the centralized and decentralized event based diagnosis approaches using formal language and automata as mode...
Globally asymptotically stable analysis in a discrete time eco-epidemiological system
International Nuclear Information System (INIS)
Hu, Zengyun; Teng, Zhidong; Zhang, Tailei; Zhou, Qiming; Chen, Xi
2017-01-01
Highlights: • Dynamical behaviors of a discrete time eco-epidemiological system are discussed. • Global asymptotical stability of this system is obtained by an iteration scheme which can be expended to general dimensional discrete system. • More complex dynamical behaviors are obtained by numerical simulations. - Abstract: In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.
System dynamics with interaction discontinuity
Luo, Albert C J
2015-01-01
This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Dynamical systems and linear algebra
Colonius, Fritz (Prof.)
2007-01-01
Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)
A Baecklund transformation between two integrable discrete hungry systems
Energy Technology Data Exchange (ETDEWEB)
Fukuda, Akiko, E-mail: j1409704@ed.kagu.tus.ac.j [Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Yamamoto, Yusaku [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Iwasaki, Masashi [Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522 (Japan); Ishiwata, Emiko [Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nakamura, Yoshimasa [Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)
2011-01-17
The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.
A Baecklund transformation between two integrable discrete hungry systems
International Nuclear Information System (INIS)
Fukuda, Akiko; Yamamoto, Yusaku; Iwasaki, Masashi; Ishiwata, Emiko; Nakamura, Yoshimasa
2011-01-01
The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.
Signatures of discrete breathers in coherent state quantum dynamics
International Nuclear Information System (INIS)
Igumenshchev, Kirill; Ovchinnikov, Misha; Prezhdo, Oleg; Maniadis, Panagiotis
2013-01-01
In classical mechanics, discrete breathers (DBs) – a spatial time-periodic localization of energy – are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space – a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes – high order tunneling modes – that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments
Dynamic modeling method for infrared smoke based on enhanced discrete phase model
Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo
2018-03-01
The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.
Thermodynamic framework for discrete optimal control in multiphase flow systems
Sieniutycz, Stanislaw
1999-08-01
Bellman's method of dynamic programming is used to synthesize diverse optimization approaches to active (work producing) and inactive (entropy generating) multiphase flow systems. Thermal machines, optimally controlled unit operations, nonlinear heat conduction, spontaneous relaxation processes, and self-propagating wave fronts are all shown to satisfy a discrete Hamilton-Jacobi-Bellman equation and a corresponding discrete optimization algorithm of Pontryagin's type, with the maximum principle for a Hamiltonian. The extremal structures are always canonical. A common unifying criterion is set for all considered systems, which is the criterion of a minimum generated entropy. It is shown that constraints can modify the entropy functionals in a different way for each group of the processes considered; thus the resulting structures of these functionals may differ significantly. Practical conclusions are formulated regarding the energy savings and energy policy in optimally controlled systems.
The magnetic flux dynamics in the critical state of one-dimensional discrete superconductor
International Nuclear Information System (INIS)
Ginzburg, S.L.; Nakin, A.V.; Savitskaya, N.E.
2006-01-01
We give a theoretical description of avalanche-like dynamics of magnetic flux in the critical state of discrete superconductors using a one-dimensional model of a multijunction SQUID. We show that the system under consideration demonstrates the self-organized criticality. The avalanches of vortices manifest themselves as jumps of the total magnetic flux in the sample. The sizes of these jumps have a power-law distribution. We argue that similarities in the behavior of discrete and usual type-II superconductors allows to extend our results for description of avalanche-like dynamics in type-II superconductors with strong pinning
Critical bifurcation surfaces of 3D discrete dynamics
Directory of Open Access Journals (Sweden)
Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Dynamic nonlinear interaction of elastic plates on discrete supports
International Nuclear Information System (INIS)
Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.
1984-01-01
A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt
Lattice fluid dynamics from perfect discretizations of continuum flows
International Nuclear Information System (INIS)
Katz, E.; Wiese, U.
1998-01-01
We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes and naturally exist on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e., grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with a square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation and is shown to represent the continuum flow exactly. For nonsquare cross sections one can use a numerical iterative procedure to derive flow equations that are approximately perfect. copyright 1998 The American Physical Society
Discrete Cosserat Approach for Multi-Section Soft Robots Dynamics
Renda, Federico; Boyer, Frederic; Dias, Jorge; Seneviratne, Lakmal
2017-01-01
In spite of recent progress, soft robotics still suffers from a lack of unified modeling framework. Nowadays, the most adopted model for the design and control of soft robots is the piece-wise constant curvature model, with its consolidated benefits and drawbacks. In this work, an alternative model for multisection soft robots dynamics is presented based on a discrete Cosserat approach, which, not only takes into account shear and torsional deformations, essentials to cope with out-of-plane e...
Discrete ergodic Jacobi matrices: Spectral properties and Quantum dynamical bounds
Han, Rui
2017-01-01
In this thesis we study discrete quasiperiodic Jacobi operators as well as ergodic operators driven by more general zero topological entropy dynamics. Such operators are deeply connected to physics (quantum Hall effect and graphene) and have enjoyed great attention from mathematics (e.g. several of Simon’s problems). The thesis has two main themes. First, to study spectral properties of quasiperiodic Jacobi matrices, in particular when off-diagonal sampling function has non-zero winding numbe...
Direct output feedback control of discrete-time systems
International Nuclear Information System (INIS)
Lin, C.C.; Chung, L.L.; Lu, K.H.
1993-01-01
An optimal direct output feedback control algorithm is developed for discrete-time systems with the consideration of time delay in control force action. Optimal constant output feedback gains are obtained through variational process such that certain prescribed quadratic performance index is minimized. Discrete-time control forces are then calculated from the multiplication of output measurements by these pre-calculated feedback gains. According to the proposed algorithm, structural system is assured to remain stable even in the presence of time delay. The number of sensors and controllers may be very small as compared with the dimension of states. Numerical results show that direct velocity feedback control is more sensitive to time delay than state feedback but, is still quite effective in reducing the dynamic responses under earthquake excitation. (author)
International Nuclear Information System (INIS)
Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C
2014-01-01
The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)
Polynomial algebra of discrete models in systems biology.
Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2010-07-01
An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.
Generalized reciprocity principle for discrete symplectic systems
Directory of Open Access Journals (Sweden)
Julia Elyseeva
2015-12-01
Full Text Available This paper studies transformations for conjoined bases of symplectic difference systems $Y_{i+1}=\\mathcal S_{i}Y_{i}$ with the symplectic coefficient matrices $\\mathcal S_i.$ For an arbitrary symplectic transformation matrix $P_{i}$ we formulate most general sufficient conditions for $\\mathcal S_{i},\\, P_{i}$ which guarantee that $P_{i}$ preserves oscillatory properties of conjoined bases $Y_{i}.$ We present examples which show that our new results extend the applicability of the discrete transformation theory.
Sternberg, Shlomo
2010-01-01
Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.""Even though there are many dynamical systems books on the market, this book is bound to become a classic. The the
Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
International Nuclear Information System (INIS)
Penney, Mark D; Koh, Dax Enshan; Spekkens, Robert W
2017-01-01
It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits. (paper)
Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.
2017-07-01
It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.
Discrete event systems in dioid algebra and conventional algebra
Declerck, Philippe
2013-01-01
This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i
A scheme for designing extreme multistable discrete dynamical ...
Indian Academy of Sciences (India)
PRIYANKA CHAKRABORTY
2017-08-21
Aug 21, 2017 ... tems [12,13], in neuron dynamics [14], in climate dynamics [15–18], in social systems [19,20] etc. A multistable dynamical system is one that possesses a large number of asymptotic stable states for a fixed set of parameters depending on initial conditions. Triv- ial multistability of a system can be considered ...
Discrete optimization in architecture extremely modular systems
Zawidzki, Machi
2017-01-01
This book is comprised of two parts, both of which explore modular systems: Pipe-Z (PZ) and Truss-Z (TZ), respectively. It presents several methods of creating PZ and TZ structures subjected to discrete optimization. The algorithms presented employ graph-theoretic and heuristic methods. The underlying idea of both systems is to create free-form structures using the minimal number of types of modular elements. PZ is more conceptual, as it forms single-branch mathematical knots with a single type of module. Conversely, TZ is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. In physical space, TZ uses two types of modules that are mirror reflections of each other. The optimization criteria discussed include: the minimal number of units, maximal adherence to the given guide paths, etc.
Applications of exterior difference systems to variations in discrete mechanics
International Nuclear Information System (INIS)
Xie Zheng; Li Hongbo
2008-01-01
In discrete mechanics, difference equations describe the fundamental physical laws and exhibit many geometric properties. Can these equations be obtained in a geometric way? Using some techniques in exterior difference systems, we investigate the discrete variational problem. As an application, we give a positive answer to the above question for the discrete Newton's, Euler-Lagrange, and Hamilton's equations
Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats
2014-05-01
In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.
On mixing property in set-valued discrete systems
International Nuclear Information System (INIS)
Gu Rongbao; Guo Wenjing
2006-01-01
Let (X,d) be a compact metric space and f:X->X be a continuous map. Let (K(X),H) be the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f-bar :K(X)->K(X) be the map defined by f-bar (A):{f(a):a-bar A}. In this paper we investigate the relationships between the mixing property of (K(X),f-bar ) and the mixing property of (X,f). In addition, we discuss specification for the set-valued discrete dynamical system (K(X),f-bar )
International Nuclear Information System (INIS)
Maruno, Ken-ichi; Biondini, Gino
2004-01-01
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Directory of Open Access Journals (Sweden)
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Sampled Data Systems Passivity and Discrete Port-Hamiltonian Systems
Stramigioli, Stefano; Secchi, Cristian; Schaft, Arjan J. van der; Fantuzzi, Cesare
2005-01-01
In this paper, we present a novel way to approach the interconnection of a continuous and a discrete time physical system. This is done in a way which preserves passivity of the coupled system independently of the sampling time T. This strategy can be used both in the field of telemanipulation, for
Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids
Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.
2009-01-01
An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.
Verifying detailed fluctuation relations for discrete feedback-controlled quantum dynamics
Camati, Patrice A.; Serra, Roberto M.
2018-04-01
Discrete quantum feedback control consists of a managed dynamics according to the information acquired by a previous measurement. Energy fluctuations along such dynamics satisfy generalized fluctuation relations, which are useful tools to study the thermodynamics of systems far away from equilibrium. Due to the practical challenge to assess energy fluctuations in the quantum scenario, the experimental verification of detailed fluctuation relations in the presence of feedback control remains elusive. We present a feasible method to experimentally verify detailed fluctuation relations for discrete feedback control quantum dynamics. Two detailed fluctuation relations are developed and employed. The method is based on a quantum interferometric strategy that allows the verification of fluctuation relations in the presence of feedback control. An analytical example to illustrate the applicability of the method is discussed. The comprehensive technique introduced here can be experimentally implemented at a microscale with the current technology in a variety of experimental platforms.
A necessary condition for dispersal driven growth of populations with discrete patch dynamics.
Guiver, Chris; Packman, David; Townley, Stuart
2017-07-07
We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.
A modified discrete element model for sea ice dynamics
Institute of Scientific and Technical Information of China (English)
LI Baohui; LI Hai; LIU Yu; WANG Anliang; JI Shunying
2014-01-01
Considering the discontinuous characteristics of sea ice on various scales, a modified discrete element mod-el (DEM) for sea ice dynamics is developed based on the granular material rheology. In this modified DEM, a soft sea ice particle element is introduced as a self-adjustive particle size function. Each ice particle can be treated as an assembly of ice floes, with its concentration and thickness changing to variable sizes un-der the conservation of mass. In this model, the contact forces among ice particles are calculated using a viscous-elastic-plastic model, while the maximum shear forces are described with the Mohr-Coulomb fric-tion law. With this modified DEM, the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths. The thicknesses, concentrations and velocities of ice particles are obtained, and then reasonable dynamic process is analyzed. The sea ice dynamic process is also simulated in a vortex wind field. Taking the influence of thermodynamics into account, this modified DEM will be improved in the future work.
Wei, Qinglai; Liu, Derong; Lin, Qiao
In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.
Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices
Hiroyuki Kasahara; Katsumi Shimotsu
2006-01-01
In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for unobserved heterogeneity. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in appli...
Butschli Dynamic Droplet System
DEFF Research Database (Denmark)
Armstrong, R.; Hanczyc, M.
2013-01-01
Dynamical oil-water systems such as droplets display lifelike properties and may lend themselves to chemical programming to perform useful work, specifically with respect to the built environment. We present Butschli water-in-oil droplets as a model for further investigation into the development...... reconstructed the Butschli system and observed its life span under a light microscope, observing chemical patterns and droplet behaviors in nearly three hundred replicate experiments. Self-organizing patterns were observed, and during this dynamic, embodied phase the droplets provided a means of introducing...... temporal and spatial order in the system with the potential for chemical programmability. The authors propose that the discrete formation of dynamic droplets, characterized by their lifelike behavior patterns, during a variable window of time (from 30 s to 30 min after the addition of alkaline water...
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)
2016-12-15
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
International Nuclear Information System (INIS)
Pham, Huyên; Wei, Xiaoli
2016-01-01
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
ADAM: analysis of discrete models of biological systems using computer algebra.
Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2011-07-20
Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web
LAN attack detection using Discrete Event Systems.
Hubballi, Neminath; Biswas, Santosh; Roopa, S; Ratti, Ritesh; Nandi, Sukumar
2011-01-01
Address Resolution Protocol (ARP) is used for determining the link layer or Medium Access Control (MAC) address of a network host, given its Internet Layer (IP) or Network Layer address. ARP is a stateless protocol and any IP-MAC pairing sent by a host is accepted without verification. This weakness in the ARP may be exploited by malicious hosts in a Local Area Network (LAN) by spoofing IP-MAC pairs. Several schemes have been proposed in the literature to circumvent these attacks; however, these techniques either make IP-MAC pairing static, modify the existing ARP, patch operating systems of all the hosts etc. In this paper we propose a Discrete Event System (DES) approach for Intrusion Detection System (IDS) for LAN specific attacks which do not require any extra constraint like static IP-MAC, changing the ARP etc. A DES model is built for the LAN under both a normal and compromised (i.e., spoofed request/response) situation based on the sequences of ARP related packets. Sequences of ARP events in normal and spoofed scenarios are similar thereby rendering the same DES models for both the cases. To create different ARP events under normal and spoofed conditions the proposed technique uses active ARP probing. However, this probing adds extra ARP traffic in the LAN. Following that a DES detector is built to determine from observed ARP related events, whether the LAN is operating under a normal or compromised situation. The scheme also minimizes extra ARP traffic by probing the source IP-MAC pair of only those ARP packets which are yet to be determined as genuine/spoofed by the detector. Also, spoofed IP-MAC pairs determined by the detector are stored in tables to detect other LAN attacks triggered by spoofing namely, man-in-the-middle (MiTM), denial of service etc. The scheme is successfully validated in a test bed. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.
Morecroft, John
System dynamics is an approach for thinking about and simulating situations and organisations of all kinds and sizes by visualising how the elements fit together, interact and change over time. This chapter, written by John Morecroft, describes modern system dynamics which retains the fundamentals developed in the 1950s by Jay W. Forrester of the MIT Sloan School of Management. It looks at feedback loops and time delays that affect system behaviour in a non-linear way, and illustrates how dynamic behaviour depends upon feedback loop structures. It also recognises improvements as part of the ongoing process of managing a situation in order to achieve goals. Significantly it recognises the importance of context, and practitioner skills. Feedback systems thinking views problems and solutions as being intertwined. The main concepts and tools: feedback structure and behaviour, causal loop diagrams, dynamics, are practically illustrated in a wide variety of contexts from a hot water shower through to a symphony orchestra and the practical application of the approach is described through several real examples of its use for strategic planning and evaluation.
Computable Types for Dynamic Systems
P.J. Collins (Pieter); K. Ambos-Spies; B. Loewe; W. Merkle
2009-01-01
textabstractIn this paper, we develop a theory of computable types suitable for the study of dynamic systems in discrete and continuous time. The theory uses type-two effectivity as the underlying computational model, but we quickly develop a type system which can be manipulated abstractly, but for
Birkhoff, George D
1927-01-01
His research in dynamics constitutes the middle period of Birkhoff's scientific career, that of maturity and greatest power. -Yearbook of the American Philosophical Society The author's great book€¦is well known to all, and the diverse active modern developments in mathematics which have been inspired by this volume bear the most eloquent testimony to its quality and influence. -Zentralblatt MATH In 1927, G. D. Birkhoff wrote a remarkable treatise on the theory of dynamical systems that would inspire many later mathematicians to do great work. To a large extent, Birkhoff was writing about his o
Local and global dynamics of Ramsey model: From continuous to discrete time.
Guzowska, Malgorzata; Michetti, Elisabetta
2018-05-01
The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.
Discrete kink dynamics in hydrogen-bonded chains: The two-component model
DEFF Research Database (Denmark)
Karpan, V.M.; Zolotaryuk, Yaroslav; Christiansen, Peter Leth
2004-01-01
We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton inte......We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion...... chain subject to a substrate with two optical bands), both providing a bistability of the hydrogen-bonded proton. Exact two-component (kink and antikink) discrete solutions for these models are found numerically. We compare the soliton solutions and their properties in both the one- (when the heavy ions...... principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist....
Kato's chaos in set-valued discrete systems
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, we investigate the relationships between Kato's chaoticity of a dynamical system (X,f) and Kato's chaoticity of the set-valued discrete system (K(X),f-bar ) associated to (X,f), where X is a compact metric space and f:X->X is a continuous map. We show that Kato's chaoticity of (K(X),f-bar ) implies the Kato's chaoticity of (X,f) in general and (X,f) is chaotic in the sense of Kato if and only if (K(X),f-bar ) is Kato chaotic in w e -topology. We also show that Ruelle-Takens' chaoticity implies Kato's chaoticity for a continuous map with a fixed point from a complete metric space without isolated point into itself
Symmetric, discrete fractional splines and Gabor systems
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2006-01-01
In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases....
Fault diagnosis for discrete event systems: Modelling and verification
International Nuclear Information System (INIS)
Simeu-Abazi, Zineb; Di Mascolo, Maria; Knotek, Michal
2010-01-01
This paper proposes an effective way for diagnosis of discrete-event systems using a timed-automaton. It is based on the model-checking technique, thanks to time analysis of the timed model. The paper proposes a method to construct all the timed models and details the different steps used to obtain the diagnosis path. A dynamic model with temporal transitions is proposed in order to model the system. By 'dynamical model', we mean an extension of timed automata for which the faulty states are identified. The model of the studied system contains the faultless functioning states and all the faulty states. Our method is based on the backward exploitation of the dynamic model, where all possible reverse paths are searched. The reverse path is the connection of the faulty state to the initial state. The diagnosis method is based on the coherence between the faulty occurrence time and the reverse path length. A real-world batch process is used to demonstrate the modelling steps and the proposed backward time analysis method to reach the diagnosis results.
Synchronization of discrete-time hyperchaotic systems: An application in communications
International Nuclear Information System (INIS)
Aguilar-Bustos, A.Y.; Cruz-Hernandez, C.
2009-01-01
In this paper, the synchronization problem of discrete-time complex dynamics is presented. In particular, we use the model-matching approach from nonlinear control theory to synchronize two unidirectionally coupled discrete-time hyperchaotic systems. A potential application to secure/private communication of confidential information is also given. By using different (hyperchaotic) encryption schemes with a single and two transmission channels, we show that output synchronization of hyperchaotic maps is indeed suitable for encryption, transmission, and decryption of information.
A spectral approach for discrete dislocation dynamics simulations of nanoindentation
Bertin, Nicolas; Glavas, Vedran; Datta, Dibakar; Cai, Wei
2018-07-01
We present a spectral approach to perform nanoindentation simulations using three-dimensional nodal discrete dislocation dynamics. The method relies on a two step approach. First, the contact problem between an indenter of arbitrary shape and an isotropic elastic half-space is solved using a spectral iterative algorithm, and the contact pressure is fully determined on the half-space surface. The contact pressure is then used as a boundary condition of the spectral solver to determine the resulting stress field produced in the simulation volume. In both stages, the mechanical fields are decomposed into Fourier modes and are efficiently computed using fast Fourier transforms. To further improve the computational efficiency, the method is coupled with a subcycling integrator and a special approach is devised to approximate the displacement field associated with surface steps. As a benchmark, the method is used to compute the response of an elastic half-space using different types of indenter. An example of a dislocation dynamics nanoindentation simulation with complex initial microstructure is presented.
A discrete dislocation dynamics model of creeping single crystals
Rajaguru, M.; Keralavarma, S. M.
2018-04-01
Failure by creep is a design limiting issue for metallic materials used in several high temperature applications. Current theoretical models of creep are phenomenological with little connection to the underlying microscopic mechanisms. In this paper, a bottom-up simulation framework based on the discrete dislocation dynamics method is presented for dislocation creep aided by the diffusion of vacancies, known to be the rate controlling mechanism at high temperature and stress levels. The time evolution of the creep strain and the dislocation microstructure in a periodic unit cell of a nominally infinite single crystal is simulated using the kinetic Monte Carlo method, together with approximate constitutive laws formulated for the rates of thermal activation of dislocations over local pinning obstacles. The deformation of the crystal due to dislocation glide between individual thermal activation events is simulated using a standard dislocation dynamics algorithm, extended to account for constant stress periodic boundary conditions. Steady state creep conditions are obtained in the simulations with the predicted creep rates as a function of stress and temperature in good agreement with experimentally reported values. Arrhenius scaling of the creep rates as a function of temperature and power-law scaling with the applied stress are also reproduced, with the values of the power-law exponents in the high stress regime in good agreement with experiments.
Cryptanalysis of a discrete-time synchronous chaotic encryption system
International Nuclear Information System (INIS)
Arroyo, David; Alvarez, Gonzalo; Li Shujun; Li Chengqing; Nunez, Juana
2008-01-01
Recently a chaotic cryptosystem based on discrete-time synchronization has been proposed. Some weaknesses of that new encryption system are addressed and exploited in order to successfully cryptanalyze the system
How to discretize differential systems in a systematic way
International Nuclear Information System (INIS)
Murata, M; Satsuma, J; Ramani, A; Grammaticos, B
2010-01-01
We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation of an exponential evolution operator. We apply our method to a host of systems for which there exist discretization results obtained by what we call the 'intuitive' method and compare the discretizations obtained. A discussion of our method as compared to one of the Mickens is also presented. Finally we apply our method to a system of coupled Riccati equations with emphasis on the preservation of the integrable character of the differential system.
Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces
International Nuclear Information System (INIS)
Höhn, Philipp A.
2014-01-01
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in the quantum theory, an according formalism for constrained variational discrete systems is constructed. While this paper focuses on global evolution moves and, for simplicity, restricts to flat configuration spaces R N , a Paper II [P. A. Höhn, “Quantization of systems with temporally varying discretization. II. Local evolution moves,” J. Math. Phys., e-print http://arxiv.org/abs/arXiv:1401.7731 [gr-qc].] discusses local evolution moves. In order to link the covariant and canonical picture, the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors. This projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums. Non-trivial coarse graining evolution moves lead to non-unitary, and thus irreversible, projections of physical Hilbert spaces and Dirac observables such that these concepts become evolution move dependent on temporally varying discretizations. The formalism is illustrated in a toy model mimicking a “creation from nothing.” Subtleties arising when applying such a formalism to quantum gravity models are discussed
An implicit finite element method for discrete dynamic fracture
Energy Technology Data Exchange (ETDEWEB)
Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Stabilization and tracking controller for a class of nonlinear discrete-time systems
International Nuclear Information System (INIS)
Sharma, B.B.; Kar, I.N.
2011-01-01
Highlights: → We present recursive design of stabilizing controller for nonlinear discrete-time systems. → Problem of stabilizing and tracking control of single link manipulator system is addressed. → We extend the proposed results to output tracking problems. → The proposed methodology is applied satisfactorily to discrete-time chaotic maps. - Abstract: In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.
Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot
Directory of Open Access Journals (Sweden)
Marcin Szuster
2014-01-01
Full Text Available Network-based control systems have been emerging technologies in the control of nonlinear systems over the past few years. This paper focuses on the implementation of the approximate dynamic programming algorithm in the network-based tracking control system of the two-wheeled mobile robot, Pioneer 2-DX. The proposed discrete tracking control system consists of the globalised dual heuristic dynamic programming algorithm, the PD controller, the supervisory term, and an additional control signal. The structure of the supervisory term derives from the stability analysis realised using the Lyapunov stability theorem. The globalised dual heuristic dynamic programming algorithm consists of two structures: the actor and the critic, realised in a form of neural networks. The actor generates the suboptimal control law, while the critic evaluates the realised control strategy by approximation of value function from the Bellman’s equation. The presented discrete tracking control system works online, the neural networks’ weights adaptation process is realised in every iteration step, and the neural networks preliminary learning procedure is not required. The performance of the proposed control system was verified by a series of computer simulations and experiments realised using the wheeled mobile robot Pioneer 2-DX.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Energy Technology Data Exchange (ETDEWEB)
Spellings, Matthew [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Marson, Ryan L. [Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Anderson, Joshua A. [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Glotzer, Sharon C., E-mail: sglotzer@umich.edu [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States)
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
An extended discrete gradient formula for oscillatory Hamiltonian systems
International Nuclear Information System (INIS)
Liu Kai; Shi Wei; Wu Xinyuan
2013-01-01
In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)
Stabilization of discrete-time LTI positive systems
Directory of Open Access Journals (Sweden)
Krokavec Dušan
2017-12-01
Full Text Available The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.
Ballard, Patrick; Charles, Alexandre
2018-03-01
In the end of the seventies, Schatzman and Moreau undertook to revisit the venerable dynamics of rigid bodies with contact and dry friction in the light of more recent mathematics. One claimed objective was to reach, for the first time, a mathematically consistent formulation of an initial value problem associated with the dynamics. The purpose of this article is to make a review of the today state-of-art concerning not only the formulation, but also the issues of existence and uniqueness of solution. xml:lang="fr"
Geometric analysis of nondeterminacy in dynamical systems
DEFF Research Database (Denmark)
Wisniewski, Rafal; Raussen, Martin Hubert
2007-01-01
This article intends to provide some new insights into concurrency using ideas from the theory of dynamical systems. Inherently discrete concurrency corresponds to a parallel continuous concept: a discrete state space corresponds to a differential manifold, an execution path corresponds to a flow...
On periodic orbits in discrete-time cascade systems
Directory of Open Access Journals (Sweden)
Huimin Li
2006-01-01
Full Text Available We present some results on existence, minimum period, number of periodic orbits, and stability of periodic orbits in discrete-time cascade systems. Some examples are presented to illustrate these results.
Reducing pressure oscillations in discrete fluid power systems
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik Clemmensen
2016-01-01
Discrete fluid power systems featuring transmission lines inherently include pressure oscillations. Experimental verification of a discrete fluid power power take off system for wave energy converters has shown the cylinder pressure to oscillate as force shifts are performed. This article investi...... investigates how cylinder pressure oscillations may be reduced by shaping the valve opening trajectory without the need for closed loop pressure feedback. Furthermore the energy costs of reducing pressure oscillations are investigated....
User interface to an ICAI system that teaches discrete math
Calcote, Roy Keith.; Howard, Richard Anthony
1990-01-01
Approved for public release; distribution is unlimited. The main thrust of this thesis is the design of a usable Intelligent Computer Aided Instruction (ICAI) user interface that does not use a natural language processor and runs on a personal computer. Discrete Mathematics is the knowledge domain for this project and the Discrete Math Tutor (DMT) is the name of the tutoring system. The DMT will allow the average student to benefit from a tutoring system now and not have to wait until the ...
On synchronized regions of discrete-time complex dynamical networks
International Nuclear Information System (INIS)
Duan Zhisheng; Chen Guanrong
2011-01-01
In this paper, the local synchronization of discrete-time complex networks is studied. First, it is shown that for any natural number n, there exists a discrete-time network which has at least left floor n/2 right floor +1 disconnected synchronized regions for local synchronization, which implies the possibility of intermittent synchronization behaviors. Different from the continuous-time networks, the existence of an unbounded synchronized region is impossible for discrete-time networks. The convexity of the synchronized regions is also characterized based on the stability of a class of matrix pencils, which is useful for enlarging the stability region so as to improve the network synchronizability.
Complex dynamics of a delayed discrete neural network of two nonidentical neurons
Energy Technology Data Exchange (ETDEWEB)
Chen, Yuanlong [Mathematics Department, GuangDong University of Finance, Guangzhou 510521 (China); Huang, Tingwen [Mathematics Department, Texas A and M University at Qatar, P. O. Box 23874, Doha (Qatar); Huang, Yu, E-mail: stshyu@mail.sysu.edu.cn [Mathematics Department, Sun Yat-Sen University, Guangzhou 510275, People' s Republic China (China)
2014-03-15
In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results.
Complex dynamics of a delayed discrete neural network of two nonidentical neurons
International Nuclear Information System (INIS)
Chen, Yuanlong; Huang, Tingwen; Huang, Yu
2014-01-01
In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results
Complex dynamics of a delayed discrete neural network of two nonidentical neurons.
Chen, Yuanlong; Huang, Tingwen; Huang, Yu
2014-03-01
In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.
Extinction in Two-Species Nonlinear Discrete Competitive System
Directory of Open Access Journals (Sweden)
Liqiong Pu
2016-01-01
Full Text Available We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.
Traveling waves in the discrete fast buffered bistable system.
Tsai, Je-Chiang; Sneyd, James
2007-11-01
We study the existence and uniqueness of traveling wave solutions of the discrete buffered bistable equation. Buffered excitable systems are used to model, among other things, the propagation of waves of increased calcium concentration, and discrete models are often used to describe the propagation of such waves across multiple cells. We derive necessary conditions for the existence of waves, and, under some restrictive technical assumptions, we derive sufficient conditions. When the wave exists it is unique and stable.
Dense time discretization technique for verification of real time systems
International Nuclear Information System (INIS)
Makackas, Dalius; Miseviciene, Regina
2016-01-01
Verifying the real-time system there are two different models to control the time: discrete and dense time based models. This paper argues a novel verification technique, which calculates discrete time intervals from dense time in order to create all the system states that can be reached from the initial system state. The technique is designed for real-time systems specified by a piece-linear aggregate approach. Key words: real-time system, dense time, verification, model checking, piece-linear aggregate
Stationary solutions and self-trapping in discrete quadratic nonlinear systems
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev
1998-01-01
We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...
A study on discrete event dynamic model for nuclear operations of main feed water pump
International Nuclear Information System (INIS)
Bae, J. C.; Choi, J. I.
2000-01-01
A major objective of the study is to propose a supervisory control algorithm based on the discrete event dynamic system (DEDS) model and apply it to the automation of nuclear operations. The study is motivated by the suitability of the DEDS model for simulation of man-made control action and the potential of the DEDS based supervisory control algorithm for enhanced licensibility, when implemented in nuclear plants, through design transparency due to strong analytic backgrounds. The DEDS model can analytically show the robust stability of the proposed supervisory controller providing design transparency for enhanced licensibility when implemented in nuclear operations
Variational discretization of the nonequilibrium thermodynamics of simple systems
Gay-Balmaz, François; Yoshimura, Hiroaki
2018-04-01
In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169–93 Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194–212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler–Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.
DEFF Research Database (Denmark)
Iskhakov, Fedor; Jørgensen, Thomas H.; Rust, John
2017-01-01
We present a fast and accurate computational method for solving and estimating a class of dynamic programming models with discrete and continuous choice variables. The solution method we develop for structural estimation extends the endogenous grid-point method (EGM) to discrete-continuous (DC) p...
Influence of discretization method on the digital control system performance
Directory of Open Access Journals (Sweden)
Futás József
2003-12-01
Full Text Available The design of control system can be divided into two steps. First the process or plant have to be convert into mathematical model form, so that its behavior can be analyzed. Then an appropriate controller have to be design in order to get the desired response of the controlled system. In the continuous time domain the system is represented by differential equations. Replacing a continuous system into discrete time form is always an approximation of the continuous system. The different discretization methods give different digital controller performance. The methods presented on the paper are Step Invariant or Zero Order Hold (ZOH Method, Matched Pole-Zero Method, Backward difference Method and Bilinear transformation. The above mentioned discretization methods are used in developing PI position controller of a dc motor. The motor model was converted by the ZOH method. The performances of the different methods are compared and the results are presented.
Hierarchical Discrete Event Supervisory Control of Aircraft Propulsion Systems
Yasar, Murat; Tolani, Devendra; Ray, Asok; Shah, Neerav; Litt, Jonathan S.
2004-01-01
This paper presents a hierarchical application of Discrete Event Supervisory (DES) control theory for intelligent decision and control of a twin-engine aircraft propulsion system. A dual layer hierarchical DES controller is designed to supervise and coordinate the operation of two engines of the propulsion system. The two engines are individually controlled to achieve enhanced performance and reliability, necessary for fulfilling the mission objectives. Each engine is operated under a continuously varying control system that maintains the specified performance and a local discrete-event supervisor for condition monitoring and life extending control. A global upper level DES controller is designed for load balancing and overall health management of the propulsion system.
System for Automatic Generation of Examination Papers in Discrete Mathematics
Fridenfalk, Mikael
2013-01-01
A system was developed for automatic generation of problems and solutions for examinations in a university distance course in discrete mathematics and tested in a pilot experiment involving 200 students. Considering the success of such systems in the past, particularly including automatic assessment, it should not take long before such systems are…
SPATIAL SEARCH IN COMMERCIAL FISHING: A DISCRETE CHOICE DYNAMIC PROGRAMMING APPROACH
Smith, Martin D.; Provencher, Bill
2003-01-01
We specify a discrete choice dynamic programming model of commercial fishing participation and location choices. This approach allows us to examine how fishermen collect information about resource abundance and whether their behavior is forward-looking.
Continuous limit of discrete systems with long-range interaction
International Nuclear Information System (INIS)
Tarasov, Vasily E
2006-01-01
Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class
Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy
Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément
2018-04-01
The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.
Human visual system automatically encodes sequential regularities of discrete events.
Kimura, Motohiro; Schröger, Erich; Czigler, István; Ohira, Hideki
2010-06-01
For our adaptive behavior in a dynamically changing environment, an essential task of the brain is to automatically encode sequential regularities inherent in the environment into a memory representation. Recent studies in neuroscience have suggested that sequential regularities embedded in discrete sensory events are automatically encoded into a memory representation at the level of the sensory system. This notion is largely supported by evidence from investigations using auditory mismatch negativity (auditory MMN), an event-related brain potential (ERP) correlate of an automatic memory-mismatch process in the auditory sensory system. However, it is still largely unclear whether or not this notion can be generalized to other sensory modalities. The purpose of the present study was to investigate the contribution of the visual sensory system to the automatic encoding of sequential regularities using visual mismatch negativity (visual MMN), an ERP correlate of an automatic memory-mismatch process in the visual sensory system. To this end, we conducted a sequential analysis of visual MMN in an oddball sequence consisting of infrequent deviant and frequent standard stimuli, and tested whether the underlying memory representation of visual MMN generation contains only a sensory memory trace of standard stimuli (trace-mismatch hypothesis) or whether it also contains sequential regularities extracted from the repetitive standard sequence (regularity-violation hypothesis). The results showed that visual MMN was elicited by first deviant (deviant stimuli following at least one standard stimulus), second deviant (deviant stimuli immediately following first deviant), and first standard (standard stimuli immediately following first deviant), but not by second standard (standard stimuli immediately following first standard). These results are consistent with the regularity-violation hypothesis, suggesting that the visual sensory system automatically encodes sequential
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Logical Discrete Event Systems in a trace theory based setting
Smedinga, R.
1993-01-01
Discrete event systems can be modelled using a triple consisting of some alphabet (representing the events that might occur), and two trace sets (sets of possible strings) denoting the possible behaviour and the completed tasks of the system. Using this definition we are able to formulate and solve
Lyapunov equation for infinite-dimensional discrete bilinear systems
International Nuclear Information System (INIS)
Costa, O.L.V.; Kubrusly, C.S.
1991-03-01
Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)
Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags
Directory of Open Access Journals (Sweden)
Liu Shengqiang
2010-01-01
Full Text Available We discuss a general -species discrete Kolmogorov system with time lags. We build some new results about the sufficient conditions for permanence, extinction, and balancing survival. When applying these results to some Lotka-Volterra systems, we obtain the criteria on harmless delay for the permanence as well as profitless delay for balancing survival.
Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags
Directory of Open Access Journals (Sweden)
Shengqiang Liu
2010-01-01
Full Text Available We discuss a general n-species discrete Kolmogorov system with time lags. We build some new results about the sufficient conditions for permanence, extinction, and balancing survival. When applying these results to some Lotka-Volterra systems, we obtain the criteria on harmless delay for the permanence as well as profitless delay for balancing survival.
Simulation of interim spent fuel storage system with discrete event model
International Nuclear Information System (INIS)
Yoon, Wan Ki; Song, Ki Chan; Lee, Jae Sol; Park, Hyun Soo
1989-01-01
This paper describes dynamic simulation of the spent fuel storage system which is described by statistical discrete event models. It visualizes flow and queue of system over time, assesses the operational performance of the system activities and establishes the system components and streams. It gives information on system organization and operation policy with reference to the design. System was tested and analyzed over a number of critical parameters to establish the optimal system. Workforce schedule and resources with long processing time dominate process. A combination of two workforce shifts a day and two cooling pits gives the optimal solution of storage system. Discrete system simulation is an useful tool to get information on optimal design and operation of the storage system. (Author)
Robust stability and ℋ ∞ -estimation for uncertain discrete systems with state-delay
Directory of Open Access Journals (Sweden)
Mahmoud Magdi S.
2001-01-01
Full Text Available In this paper, we investigate the problems of robust stability and ℋ ∞ -estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteed ℋ ∞ -performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.
Discretization of superintegrable systems on a plane
Kabát, Z.
2012-02-01
We construct difference analogues of so called Smorodinsky-Winternitz superintegrable systems in the Euclidean plane. Using methods of umbral calculus, we obtain difference equations for generalized isotropic harmonic oscillator on the uniform lattice, and also its solution in terms of power series. In the case of gauge-rotated Hamiltonian, the solution is a polynomial, well-defined in the whole plane.
PREFACE: Continuum Models and Discrete Systems Symposia (CMDS-12)
Chakrabarti, Bikas K.
2011-09-01
of interest were: Thermodynamics, transport theory and statistical mechanics in the context of continuum modeling discrete systems; Statistical mechanics and dynamics of fluid flows; Continuum mechanics of complex fluids and deformable solids with microstructure; Fundamentals of fracture, defect dynamics, fatigue, and fracture dynamics; Statics and dynamics of dislocations, dislocation mediated phase transitions and plasticity; Granular materials: statics and dynamics; Physics and mechanics of earthquakes; Transport in composite materials; and Continuum theory of soft matter systems of biological motivation and living structures. The scientific program consisted of General Lectures and Research Communications. The four General Lectures (40 min + 5 min) introduced the most recent ideas and advances in the fields covered. The 25 Research Communications reported new results and methods in these fields and were presented orally (30 min + 5 min). In addition there were 15 posters which also presented interesting results and five of these posters were selected by a special committee chaired by David J Bergman to contribute to this proceedings. The selected five posters were presented by Moutushi D Choudhury, Morten Grova, Arya Paul, Arnab Saha and Amartya Sarkar. We were happy to note that 32 scientists from ten countries and a large number of students (both from India and other countries) participated in this symposium. The talks and poster sessions generated a lot of discussions, arguments and collaborations. The articles that appear in this proceedings are based on the invited talks and selected poster presentations. We would like to thank the Journal of Physics Conference Series (IOP Publishing) for publishing the proceedings of the conference. We would also like to thank all the contributors to this proceedings for their kind co-operation and the referees for their prompt and active support. A number of invited participants (Amit Acharya, Alexander Altland, Kamal K
Risk-based design of process systems using discrete-time Bayesian networks
International Nuclear Information System (INIS)
Khakzad, Nima; Khan, Faisal; Amyotte, Paul
2013-01-01
Temporal Bayesian networks have gained popularity as a robust technique to model dynamic systems in which the components' sequential dependency, as well as their functional dependency, cannot be ignored. In this regard, discrete-time Bayesian networks have been proposed as a viable alternative to solve dynamic fault trees without resort to Markov chains. This approach overcomes the drawbacks of Markov chains such as the state-space explosion and the error-prone conversion procedure from dynamic fault tree. It also benefits from the inherent advantages of Bayesian networks such as probability updating. However, effective mapping of the dynamic gates of dynamic fault trees into Bayesian networks while avoiding the consequent huge multi-dimensional probability tables has always been a matter of concern. In this paper, a new general formalism has been developed to model two important elements of dynamic fault tree, i.e., cold spare gate and sequential enforcing gate, with any arbitrary probability distribution functions. Also, an innovative Neutral Dependency algorithm has been introduced to model dynamic gates such as priority-AND gate, thus reducing the dimension of conditional probability tables by an order of magnitude. The second part of the paper is devoted to the application of discrete-time Bayesian networks in the risk assessment and safety analysis of complex process systems. It has been shown how dynamic techniques can effectively be applied for optimal allocation of safety systems to obtain maximum risk reduction.
Invariant set computation for constrained uncertain discrete-time systems
Athanasopoulos, N.; Bitsoris, G.
2010-01-01
In this article a novel approach to the determination of polytopic invariant sets for constrained discrete-time linear uncertain systems is presented. First, the problem of stabilizing a prespecified initial condition set in the presence of input and state constraints is addressed. Second, the
Hybrid modelling in discrete-event control system design
Beek, van D.A.; Rooda, J.E.; Gordijn, S.H.F.; Borne, P.
1996-01-01
Simulation-based testing of discrete-event control systems can be advantageous. There is, however, a considerable difference between languages for real-time control and simulation languages. The Chi language, presented in this paper, is suited to specification and simulation of real-time control
On the discretization of linear fractional representations of LPV systems
Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.
2012-01-01
Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a
Cryptanalyzing a discrete-time chaos synchronization secure communication system
International Nuclear Information System (INIS)
Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.
2004-01-01
This paper describes the security weakness of a recently proposed secure communication method based on discrete-time chaos synchronization. We show that the security is compromised even without precise knowledge of the chaotic system used. We also make many suggestions to improve its security in future versions
Modular Control of Discrete-Event Systems with Coalgebra
Czech Academy of Sciences Publication Activity Database
Komenda, Jan; van Schuppen, J. H.
2008-01-01
Roč. 53, č. 2 (2008), s. 447-460 ISSN 0018-9286 R&D Projects: GA AV ČR(CZ) KJB100190609 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete-event systems * modular supervisory control * coalgebra Subject RIV: BA - General Mathematics Impact factor: 3.293, year: 2008
Directory of Open Access Journals (Sweden)
V. Gontar
2000-01-01
Full Text Available Based on discrete chaotic dynamics algorithms different patterns in a form of mandalas have been generated. This fact gives us the possibility to make a link between mechanism of biochemical reaction dynamics undergoing in brain resulted to the brain creativity process in form of mandalas. Obtained patterns can be related to the space distributed chemicals according to the law of extended principle of maximum entropy, consideration of the information exchange during biochemical transformations, mass conservation law and discrete chaotic dynamics principles.
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...
The dynamics of discrete populations and series of events
Hopcraft, Keith Iain; Ridley, Kevin D
2014-01-01
IntroductionReferencesStatistical PreliminariesIntroductionProbability DistributionsMoment-Generating FunctionsDiscrete ProcessesSeries of EventsSummaryFurther ReadingMarkovian Population ProcessesIntroductionBirths and DeathsImmigration and the Poisson ProcessThe Effect of MeasurementCorrelation of CountsSummaryFurther ReadingThe Birth-Death-Immigration ProcessIntroductionRate Equations for the ProcessEquation for the Generating FunctionGeneral Time-Dependent SolutionFluctuation Characteristics of a Birth-Death-Immigration PopulationSampling and Measurement ProcessesCorrelation of CountsSumma
Energy Cost of Avoiding Pressure Oscillations in a Discrete Fluid Power Force System
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik Clemmensen
2015-01-01
In secondary valve controlled discrete fluid power force systems the valve opening trajectory greatly influences the pressure dynamics in the actuator chambers. For discrete fluid power systems featuring hoses of significant length pressure oscillations due to fast valve switching is well......-known. This paper builds upon theoretical findings on how shaping of the valve opening may reduce the cylinder pressure oscillations. The current paper extents the work by implementing the valve opening characteristics reducing the pressure oscillations on a full scale power take-off test-bench for wave energy...... will present measurements comparing pressure dynamics for two valve opening algorithms. In addition the paper will give a theoretical investigation of the energy loss during valve shifting and finally measurements of average power output from the power take-off system in various sea states are compared...
DEFF Research Database (Denmark)
Thomsen, Per Grove
1996-01-01
A one-dimensional model with axial discretization of engine components has been formulated using tha balance equations for mass energy and momentum and the ideal gas equation of state. ODE's that govern the dynamic behaviour of the regenerator matrix temperatures are included in the model. Known...
Liu, Nan; Wen, Xiao-Yong
2018-03-01
Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.
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.
A representation theorem for linear discrete-space systems
Directory of Open Access Journals (Sweden)
Sandberg Irwin W.
1998-01-01
Full Text Available The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.
Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
Extinction dynamics of a discrete population in an oasis.
Berti, Stefano; Cencini, Massimo; Vergni, Davide; Vulpiani, Angelo
2015-07-01
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here we introduce an individual-based analog of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasistationary distribution of the number of individuals for patch sizes above the critical threshold.
A study of the dynamics of a discrete auroral arc
International Nuclear Information System (INIS)
Marklund, G.; Sandahl, I.; Opgenoorth, H.
1981-06-01
High resolution electric field and particle data, obtained by the S23L1 rocket crossing over a discrete prebreakup arc in January 1979, are studied in coordination with ground observations in order to clarify the electrodynamics of the arc and its surroundings. Height-integrated conductivities have been calculated from the particle data, including the ionization effect of precipitating protons, and assuming a steady state balance between ion production and recombination losses. High resolution optical information of arc location relative to the rocket permitted a check of the validity of this assumption for each fluxtube passed by the rocket. Another check was provided by a comparison between calculated and observed electron densities along the rocket trajectory. (author)
Navier-Stokes Dynamics by a Discrete Boltzmann Model
Rubinstein, Robet
2010-01-01
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
Generalized Synchronization of Time-Delayed Discrete Systems
International Nuclear Information System (INIS)
Jing Jianyi; Min Lequan
2009-01-01
This paper establishes two theorems for two time-delayed (chaotic) discrete systems to achieve time-delayed generalized synchronization (TDGS). These two theorems uncover the general forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems. (interdisciplinary physics and related areas of science and technology)
International Nuclear Information System (INIS)
Kang, Li; Tang, Sanyi
2016-01-01
Highlights: • The discrete single species and multiple species models with random perturbation are proposed. • The complex dynamics and interesting bifurcation behavior have been investigated. • The reverse effects of random perturbation on discrete systems have been discussed and revealed. • The main results can be applied for pest control and resources management. - Abstract: The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.
Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests
Richardson, Derek C.; Walsh, Kevin J.; Murdoch, Naomi; Michel, Patrick
2011-03-01
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular “atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to centrifuging as a function of rotation rate.
Enhanced Discrete-Time Scheduler Engine for MBMS E-UMTS System Level Simulator
DEFF Research Database (Denmark)
Pratas, Nuno; Rodrigues, António
2007-01-01
In this paper the design of an E-UMTS system level simulator developed for the study of optimization methods for the MBMS is presented. The simulator uses a discrete event based philosophy, which captures the dynamic behavior of the Radio Network System. This dynamic behavior includes the user...... mobility, radio interfaces and the Radio Access Network. Its given emphasis on the enhancements developed for the simulator core, the Event Scheduler Engine. Two implementations for the Event Scheduler Engine are proposed, one optimized for single core processors and other for multi-core ones....
Lemrich, Laure; Carmeliet, Jan; Johnson, Paul A.; Guyer, Robert; Jia, Xiaoping
2017-12-01
A granular system composed of frictional glass beads is simulated using the discrete element method. The intergrain forces are based on the Hertz contact law in the normal direction with frictional tangential force. The damping due to collision is also accounted for. Systems are loaded at various stresses and their quasistatic elastic moduli are characterized. Each system is subjected to an extensive dynamic testing protocol by measuring the resonant response to a broad range of ac drive amplitudes and frequencies via a set of diagnostic strains. The system, linear at small ac drive amplitudes, has resonance frequencies that shift downward (i.e., modulus softening) with increased ac drive amplitude. Detailed testing shows that the slipping contact ratio does not contribute significantly to this dynamic modulus softening, but the coordination number is strongly correlated to this reduction. This suggests that the softening arises from the extended structural change via break and remake of contacts during the rearrangement of bead positions driven by the ac amplitude.
A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops.
Directory of Open Access Journals (Sweden)
Réka Albert
2017-09-01
Full Text Available Stomata, microscopic pores in leaf surfaces through which water loss and carbon dioxide uptake occur, are closed in response to drought by the phytohormone abscisic acid (ABA. This process is vital for drought tolerance and has been the topic of extensive experimental investigation in the last decades. Although a core signaling chain has been elucidated consisting of ABA binding to receptors, which alleviates negative regulation by protein phosphatases 2C (PP2Cs of the protein kinase OPEN STOMATA 1 (OST1 and ultimately results in activation of anion channels, osmotic water loss, and stomatal closure, over 70 additional components have been identified, yet their relationships with each other and the core components are poorly elucidated. We integrated and processed hundreds of disparate observations regarding ABA signal transduction responses underlying stomatal closure into a network of 84 nodes and 156 edges and, as a result, established those relationships, including identification of a 36-node, strongly connected (feedback-rich component as well as its in- and out-components. The network's domination by a feedback-rich component may reflect a general feature of rapid signaling events. We developed a discrete dynamic model of this network and elucidated the effects of ABA plus knockout or constitutive activity of 79 nodes on both the outcome of the system (closure and the status of all internal nodes. The model, with more than 1024 system states, is far from fully determined by the available data, yet model results agree with existing experiments in 82 cases and disagree in only 17 cases, a validation rate of 75%. Our results reveal nodes that could be engineered to impact stomatal closure in a controlled fashion and also provide over 140 novel predictions for which experimental data are currently lacking. Noting the paucity of wet-bench data regarding combinatorial effects of ABA and internal node activation, we experimentally confirmed
A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops.
Albert, Réka; Acharya, Biswa R; Jeon, Byeong Wook; Zañudo, Jorge G T; Zhu, Mengmeng; Osman, Karim; Assmann, Sarah M
2017-09-01
Stomata, microscopic pores in leaf surfaces through which water loss and carbon dioxide uptake occur, are closed in response to drought by the phytohormone abscisic acid (ABA). This process is vital for drought tolerance and has been the topic of extensive experimental investigation in the last decades. Although a core signaling chain has been elucidated consisting of ABA binding to receptors, which alleviates negative regulation by protein phosphatases 2C (PP2Cs) of the protein kinase OPEN STOMATA 1 (OST1) and ultimately results in activation of anion channels, osmotic water loss, and stomatal closure, over 70 additional components have been identified, yet their relationships with each other and the core components are poorly elucidated. We integrated and processed hundreds of disparate observations regarding ABA signal transduction responses underlying stomatal closure into a network of 84 nodes and 156 edges and, as a result, established those relationships, including identification of a 36-node, strongly connected (feedback-rich) component as well as its in- and out-components. The network's domination by a feedback-rich component may reflect a general feature of rapid signaling events. We developed a discrete dynamic model of this network and elucidated the effects of ABA plus knockout or constitutive activity of 79 nodes on both the outcome of the system (closure) and the status of all internal nodes. The model, with more than 1024 system states, is far from fully determined by the available data, yet model results agree with existing experiments in 82 cases and disagree in only 17 cases, a validation rate of 75%. Our results reveal nodes that could be engineered to impact stomatal closure in a controlled fashion and also provide over 140 novel predictions for which experimental data are currently lacking. Noting the paucity of wet-bench data regarding combinatorial effects of ABA and internal node activation, we experimentally confirmed several predictions
Directory of Open Access Journals (Sweden)
Yiming Jiang
2016-01-01
Full Text Available Over the last few decades, the intelligent control methods such as fuzzy logic control (FLC and neural network (NN control have been successfully used in various applications. The rapid development of digital computer based control systems requires control signals to be calculated in a digital or discrete-time form. In this background, the intelligent control methods developed for discrete-time systems have drawn great attentions. This survey aims to present a summary of the state of the art of the design of FLC and NN-based intelligent control for discrete-time systems. For discrete-time FLC systems, numerous remarkable design approaches are introduced and a series of efficient methods to deal with the robustness, stability, and time delay of FLC discrete-time systems are recommended. Techniques for NN-based intelligent control for discrete-time systems, such as adaptive methods and adaptive dynamic programming approaches, are also reviewed. Overall, this paper is devoted to make a brief summary for recent progresses in FLC and NN-based intelligent control design for discrete-time systems as well as to present our thoughts and considerations of recent trends and potential research directions in this area.
Stability of molecular dynamics simulations of classical systems
DEFF Research Database (Denmark)
Toxværd, Søren
2012-01-01
The existence of a shadow Hamiltonian for discrete classical dynamics, obtained by an asymptotic expansion for a discrete symplectic algorithm, is employed to determine the limit of stability for molecular dynamics (MD) simulations with respect to the time-increment h of the discrete dynamics....... The investigation is based on the stability of the shadow energy, obtained by including the first term in the asymptotic expansion, and on the exact solution of discrete dynamics for a single harmonic mode. The exact solution of discrete dynamics for a harmonic potential with frequency ω gives a criterion...... for the limit of stability h ⩽ 2/ω. Simulations of the Lennard-Jones system and the viscous Kob-Andersen system show that one can use the limit of stability of the shadow energy or the stability criterion for a harmonic mode on the spectrum of instantaneous frequencies to determine the limit of stability of MD...
Application of network methods for understanding evolutionary dynamics in discrete habitats.
Greenbaum, Gili; Fefferman, Nina H
2017-06-01
In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.
Chaos and its synchronization in two-neuron systems with discrete delays
International Nuclear Information System (INIS)
Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo
2004-01-01
It is well known that complex dynamic behaviors exist in time-delayed neural systems. Infinite positive Lyapunov exponents can be found in time-delayed chaotic systems since the dimension of such systems is infinite. However, theoretical and experimental models studied thus far are low dimensional systems with only one positive Lyapunov exponent. Consequently, messages masked by such chaotic systems are shown to be easily extracted in some cases. Therefore, communication system with a higher security level can be design by means of the time-delayed neuron systems. In this paper, we firstly investigate the dynamical behaviors of two-neuron systems with discrete delays. Then, the chaos synchronization in time-delayed neuron system is studied based on the method of designing the coupled system and employing Krasovskii-Lyapunov theory to search the synchronization conditions. Numerical results illustrate the correctness of our theoretical analyses
Global consensus for discrete-time competitive systems
International Nuclear Information System (INIS)
Shih, C.-W.; Tseng, J.-P.
2009-01-01
Grossberg established a remarkable convergence theorem for a class of competitive systems without knowing and using Lyapunov function for the systems. We present the parallel investigations for the discrete-time version of the Grossberg's model. Through developing an extended component-competing analysis for the coupled system, without knowing a Lyapunov function and applying the LaSalle's invariance principle, the global pattern formation or the so-called global consensus for the system can be achieved. A numerical simulation is performed to illustrate the present theory.
Complexity of deciding detectability in discrete event systems
Czech Academy of Sciences Publication Activity Database
Masopust, Tomáš
2018-01-01
Roč. 93, July (2018), s. 257-261 ISSN 0005-1098 Institutional support: RVO:67985840 Keywords : discrete event systems * finite automata * detectability Subject RIV: BA - General Mathematics OBOR OECD: Computer science s, information science , bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 5.451, year: 2016 https://www. science direct.com/ science /article/pii/S0005109818301730
H 2 guaranteed cost control of discrete linear systems
Directory of Open Access Journals (Sweden)
Colmenares W.
2000-01-01
Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.
Complexity of deciding detectability in discrete event systems
Czech Academy of Sciences Publication Activity Database
Masopust, Tomáš
2018-01-01
Roč. 93, July (2018), s. 257-261 ISSN 0005-1098 Institutional support: RVO:67985840 Keywords : discrete event systems * finite automata * detectability Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 5.451, year: 2016 https://www.sciencedirect.com/science/article/pii/S0005109818301730
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
Directory of Open Access Journals (Sweden)
J. Schachenmayer
2015-02-01
Full Text Available Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.
Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers
International Nuclear Information System (INIS)
Rahman, Aminur; Blackmore, Denis
2016-01-01
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark–Sacker (N–S) bifurcations, and even chaos. For example, in [1], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one- dimensional path model. We prove Gilet’s conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.
State transformations and Hamiltonian structures for optimal control in discrete systems
Sieniutycz, S.
2006-04-01
Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.
Discrete Wavelet Transform for Fault Locations in Underground Distribution System
Apisit, C.; Ngaopitakkul, A.
2010-10-01
In this paper, a technique for detecting faults in underground distribution system is presented. Discrete Wavelet Transform (DWT) based on traveling wave is employed in order to detect the high frequency components and to identify fault locations in the underground distribution system. The first peak time obtained from the faulty bus is employed for calculating the distance of fault from sending end. The validity of the proposed technique is tested with various fault inception angles, fault locations and faulty phases. The result is found that the proposed technique provides satisfactory result and will be very useful in the development of power systems protection scheme.
Discrete event simulation versus conventional system reliability analysis approaches
DEFF Research Database (Denmark)
Kozine, Igor
2010-01-01
Discrete Event Simulation (DES) environments are rapidly developing and appear to be promising tools for building reliability and risk analysis models of safety-critical systems and human operators. If properly developed, they are an alternative to the conventional human reliability analysis models...... and systems analysis methods such as fault and event trees and Bayesian networks. As one part, the paper describes briefly the author’s experience in applying DES models to the analysis of safety-critical systems in different domains. The other part of the paper is devoted to comparing conventional approaches...
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik C.
2014-01-01
Discrete fluid power technology attracts great attention because it enables energy efficiency and robust system architectures. However, the discrete nature of this technology naturally brings shifting phenomenons into the picture. For fluid power system the relative high inductance of fluid...
Liao, Bolin; Zhang, Yunong; Jin, Long
2016-02-01
In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.
Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems
International Nuclear Information System (INIS)
Li Yin; Chen Yong; Li Biao
2009-01-01
This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.
Simulation of dynamic systems with Matlab and Simulink
Klee, Harold
2011-01-01
Mathematical ModelingDerivation of a Mathematical ModelDifference EquationsFirst Look at Discrete-Time SystemsCase Study: Population Dynamics (Single Species)Continuous-Time SystemsFirst-Order SystemsSecond-Order SystemsSimulation DiagramsHigher-Order SystemsState VariablesNonlinear SystemsCase Study: Submarine Depth Control SystemElementary Numerical IntegrationDiscrete-Time System Approximation of a Continuous-
Guay, M.; Beerens, R.; Nijmeijer, H.
2014-01-01
This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and
Safety Discrete Event Models for Holonic Cyclic Manufacturing Systems
Ciufudean, Calin; Filote, Constantin
In this paper the expression “holonic cyclic manufacturing systems” refers to complex assembly/disassembly systems or fork/join systems, kanban systems, and in general, to any discrete event system that transforms raw material and/or components into products. Such a system is said to be cyclic if it provides the same sequence of products indefinitely. This paper considers the scheduling of holonic cyclic manufacturing systems and describes a new approach using Petri nets formalism. We propose an approach to frame the optimum schedule of holonic cyclic manufacturing systems in order to maximize the throughput while minimize the work in process. We also propose an algorithm to verify the optimum schedule.
Robust performance results for discrete-time systems
Directory of Open Access Journals (Sweden)
Mahmoud Magdi S.
1997-01-01
Full Text Available The problems of robust performance and feedback control synthesis for a class of linear discrete-time systems with time-varying parametric uncertainties are addressed in this paper. The uncertainties are bound and have a linear matrix fractional form. Based on the concept of strongly robust H ∞ -performance criterion, results of robust stability and performance are developed and expressed in easily computable linear matrix inequalities. Synthesis of robust feedback controllers is carried out for several system models of interest.
Discrete simulation system based on artificial intelligence methods
Energy Technology Data Exchange (ETDEWEB)
Futo, I; Szeredi, J
1982-01-01
A discrete event simulation system based on the AI language Prolog is presented. The system called t-Prolog extends the traditional possibilities of simulation languages toward automatic problem solving by using backtrack in time and automatic model modification depending on logical deductions. As t-Prolog is an interactive tool, the user has the possibility to interrupt the simulation run to modify the model or to force it to return to a previous state for trying possible alternatives. It admits the construction of goal-oriented or goal-seeking models with variable structure. Models are defined in a restricted version of the first order predicate calculus using Horn clauses. 21 references.
Frequency interval balanced truncation of discrete-time bilinear systems
DEFF Research Database (Denmark)
Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza
2016-01-01
This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals...... are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new...... generalized frequency interval controllability and observability gramians as part of the balanced truncation framework are provided to demonstrate the performance of the proposed method....
Simulating continuous-time Hamiltonian dynamics by way of a discrete-time quantum walk
International Nuclear Information System (INIS)
Schmitz, A.T.; Schwalm, W.A.
2016-01-01
Much effort has been made to connect the continuous-time and discrete-time quantum walks. We present a method for making that connection for a general graph Hamiltonian on a bigraph. Furthermore, such a scheme may be adapted for simulating discretized quantum models on a quantum computer. A coin operator is found for the discrete-time quantum walk which exhibits the same dynamics as the continuous-time evolution. Given the spectral decomposition of the graph Hamiltonian and certain restrictions, the discrete-time evolution is solved for explicitly and understood at or near important values of the parameters. Finally, this scheme is connected to past results for the 1D chain. - Highlights: • A discrete-time quantum walk is purposed which approximates a continuous-time quantum walk. • The purposed quantum walk could be used to simulate Hamiltonian dynamics on a quantum computer. • Given the spectra decomposition of the Hamiltonian, the quantum walk is solved explicitly. • The method is demonstrated and connected to previous work done on the 1D chain.
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro
2011-01-01
We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)
Nonlinear dynamical system approaches towards neural prosthesis
International Nuclear Information System (INIS)
Torikai, Hiroyuki; Hashimoto, Sho
2011-01-01
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
A Family of Integrable Rational Semi-Discrete Systems and Its Reduction
International Nuclear Information System (INIS)
Xu Xixiang
2010-01-01
Within framework of zero curvature representation theory, a family of integrahle rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out. (general)
International Nuclear Information System (INIS)
Ferdowsi, B.
2014-01-01
Recent seismological observations based on new, more sensitive instrumentation show that seismic waves radiated from large earthquakes can trigger other earthquakes globally. This phenomenon is called dynamic earthquake triggering and is well-documented for over 30 of the largest earthquakes worldwide. Granular materials are at the core of mature earthquake faults and play a key role in fault triggering by exhibiting a rich nonlinear response to external perturbations. The stick-slip dynamics in sheared granular layers is analogous to the seismic cycle for earthquake fault systems. In this research effort, we characterize the macroscopic scale statistics and the grain-scale mechanisms of triggered slip in sheared granular layers. We model the granular fault gouge using three dimensional discrete element method simulations. The modeled granular system is put into stick-slip dynamics by applying a conning pressure and a shear load. The dynamic triggering is simulated by perturbing the spontaneous stick-slip dynamics using an external vibration applied to the boundary of the layer. The influences of the triggering consist in a frictional weakening during the vibration interval, a clock advance of the next expected large slip event and long term effects in the form of suppression and recovery of the energy released from the granular layer. Our study suggests that above a critical amplitude, vibration causes a significant clock advance of large slip events. We link this clock advance to a major decline in the slipping contact ratio as well as a decrease in shear modulus and weakening of the granular gouge layer. We also observe that shear vibration is less effective in perturbing the stick-slip dynamics of the granular layer. Our study suggests that in order to have an effective triggering, the input vibration must also explore the granular layer at length scales about or less than the average grain size. The energy suppression and the subsequent recovery and increased
A discrete force allocation algorithm for modelling wind turbines in computational fluid dynamics
DEFF Research Database (Denmark)
Réthoré, Pierre-Elouan; Sørensen, Niels N.
2012-01-01
at the position of the wind turbine rotor to estimate correctly the power production and the rotor loading. The method proposed in this paper solves this issue by spreading the force on the direct neighbouring cells and applying an equivalent pressure jump at the cell faces. This can potentially open......This paper describes an algorithm for allocating discrete forces in computational fluid dynamics (CFD). Discrete forces are useful in wind energy CFD. They are used as an approximation of the wind turbine blades’ action on the wind (actuator disc/line), to model forests and to model turbulent...
Dynamics of a two-dimensional discrete-time SIS model
Directory of Open Access Journals (Sweden)
Jaime H. Barrera
2012-04-01
Full Text Available We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation, which enables us to reduce the system of, two-equations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (Ro is less than one and greater than one, respectively. When we consider a non-constant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the occurrence of a strange attractor.
Six-component semi-discrete integrable nonlinear Schrödinger system
Vakhnenko, Oleksiy O.
2018-01-01
We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.
Consensus of Discrete Multiagent System with Various Time Delays and Environmental Disturbances
Directory of Open Access Journals (Sweden)
Zheping Yan
2014-12-01
Full Text Available In this paper, the consensus problem of discrete multiagent systems with time varying sampling periods is studied. Firstly, with thorough analysis of various delays among agents, the control input of each agent is designed with consideration of sending delay and receiving delay. With construction of discrete dynamics of state error vector, it is proved by applying Halanay inequality that consensus of the system can be reached. Further, the definition of bounded consensus is proposed in the situation where environmental disturbances exist. In order to handle this problem, the Halanay inequality is extended into a more general one with boundedness property. Based on the new Halanay inequality obtained, the boundedness of consensus error is guaranteed. At last, simulation examples are presented to demonstrate the theoretical conclusions.
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.
Discrete opinion dynamics on networks based on social influence
International Nuclear Information System (INIS)
Hu Haibo; Wang Xiaofan
2009-01-01
A model of opinion dynamics based on social influence on networks was studied. The opinion of each agent can have integer values i = 1, 2, ..., I and opinion exchanges are restricted to connected agents. It was found that for any I ≥ 2 and self-confidence parameter 0 ≤ u i ) of the population that hold a given opinion i is a martingale, and the fraction q i of opinion i will gradually converge to (q i ). The tendency can slow down with the increase of degree assortativity of networks. When u is degree dependent, (q i ) does not possess the martingale property, however q i still converges to it. In both cases for a finite network the states of all agents will finally reach consensus. Further if there exist stubborn persons in the population whose opinions do not change over time, it was found that for degree-independent constant u, both q i and (q i ) will converge to fixed proportions which only depend on the distribution of initial obstinate persons, and naturally the final equilibrium state will be the coexistence of diverse opinions held by the stubborn people. The analytical results were verified by numerical simulations on Barabasi-Albert (BA) networks. The model highlights the influence of high-degree agents on the final consensus or coexistence state and captures some realistic features of the diffusion of opinions in social networks
Dynamical barrier for the formation of solitary waves in discrete lattices
International Nuclear Information System (INIS)
Kevrekidis, P.G.; Espinola-Rocha, J.A.; Drossinos, Y.; Stefanov, A.
2008-01-01
We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation
Dynamical barrier for the formation of solitary waves in discrete lattices
Energy Technology Data Exchange (ETDEWEB)
Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States)], E-mail: kevrekid@math.umass.edu; Espinola-Rocha, J.A. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States); Drossinos, Y. [European Commission, Joint Research Centre, I-21020 Ispra (Vatican City State, Holy See,) (Italy); School of Mechanical and Systems Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU (United Kingdom); Stefanov, A. [Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS 66045-7523 (United States)
2008-03-24
We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation.
Discrete two-sex models of population dynamics: On modelling the mating function
Bessa-Gomes, Carmen; Legendre, Stéphane; Clobert, Jean
2010-09-01
Although sexual reproduction has long been a central subject of theoretical ecology, until recently its consequences for population dynamics were largely overlooked. This is now changing, and many studies have addressed this issue, showing that when the mating system is taken into account, the population dynamics depends on the relative abundance of males and females, and is non-linear. Moreover, sexual reproduction increases the extinction risk, namely due to the Allee effect. Nevertheless, different studies have identified diverse potential consequences, depending on the choice of mating function. In this study, we investigate the consequences of three alternative mating functions that are frequently used in discrete population models: the minimum; the harmonic mean; and the modified harmonic mean. We consider their consequences at three levels: on the probability that females will breed; on the presence and intensity of the Allee effect; and on the extinction risk. When we consider the harmonic mean, the number of times the individuals of the least abundant sex mate exceeds their mating potential, which implies that with variable sex-ratios the potential reproductive rate is no longer under the modeller's control. Consequently, the female breeding probability exceeds 1 whenever the sex-ratio is male-biased, which constitutes an obvious problem. The use of the harmonic mean is thus only justified if we think that this parameter should be re-defined in order to represent the females' breeding rate and the fact that females may reproduce more than once per breeding season. This phenomenon buffers the Allee effect, and reduces the extinction risk. However, when we consider birth-pulse populations, such a phenomenon is implausible because the number of times females can reproduce per birth season is limited. In general, the minimum or modified harmonic mean mating functions seem to be more suitable for assessing the impact of mating systems on population dynamics.
Control of discrete event systems modeled as hierarchical state machines
Brave, Y.; Heymann, M.
1991-01-01
The authors examine a class of discrete event systems (DESs) modeled as asynchronous hierarchical state machines (AHSMs). For this class of DESs, they provide an efficient method for testing reachability, which is an essential step in many control synthesis procedures. This method utilizes the asynchronous nature and hierarchical structure of AHSMs, thereby illustrating the advantage of the AHSM representation as compared with its equivalent (flat) state machine representation. An application of the method is presented where an online minimally restrictive solution is proposed for the problem of maintaining a controlled AHSM within prescribed legal bounds.
Optimal Robust Fault Detection for Linear Discrete Time Systems
Directory of Open Access Journals (Sweden)
Nike Liu
2008-01-01
Full Text Available This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such as ℋ−/ℋ∞, ℋ2/ℋ∞, and ℋ∞/ℋ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal but useless fault-detection filters.
A parametric LTR solution for discrete-time systems
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Jannerup, Ole Erik
1989-01-01
A parametric LTR (loop transfer recovery) solution for discrete-time compensators incorporating filtering observers which achieve exact recovery is presented for both minimum- and non-minimum-phase systems. First the recovery error, which defines the difference between the target loop transfer...... and the full loop transfer function, is manipulated into a general form involving the target loop transfer matrix and the fundamental recovery matrix. A parametric LTR solution based on the recovery matrix is developed. It is shown that the LQR/LTR (linear quadratic Gaussian/loop transfer recovery) solution...
Discrete opinion dynamics on networks based on social influence
Energy Technology Data Exchange (ETDEWEB)
Hu Haibo; Wang Xiaofan [Complex Networks and Control Lab, Shanghai Jiao Tong University, Shanghai 200240 (China)
2009-06-05
A model of opinion dynamics based on social influence on networks was studied. The opinion of each agent can have integer values i = 1, 2, ..., I and opinion exchanges are restricted to connected agents. It was found that for any I {>=} 2 and self-confidence parameter 0 {<=} u < 1, when u is a degree-independent constant, the weighted proportion (q{sub i}) of the population that hold a given opinion i is a martingale, and the fraction q{sub i} of opinion i will gradually converge to (q{sub i}). The tendency can slow down with the increase of degree assortativity of networks. When u is degree dependent, (q{sub i}) does not possess the martingale property, however q{sub i} still converges to it. In both cases for a finite network the states of all agents will finally reach consensus. Further if there exist stubborn persons in the population whose opinions do not change over time, it was found that for degree-independent constant u, both q{sub i} and (q{sub i}) will converge to fixed proportions which only depend on the distribution of initial obstinate persons, and naturally the final equilibrium state will be the coexistence of diverse opinions held by the stubborn people. The analytical results were verified by numerical simulations on Barabasi-Albert (BA) networks. The model highlights the influence of high-degree agents on the final consensus or coexistence state and captures some realistic features of the diffusion of opinions in social networks.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Hybrid dynamical systems observation and control
Defoort, Michael
2015-01-01
This book is a collection of contributions defining the state of current knowledge and new trends in hybrid systems – systems involving both continuous dynamics and discrete events – as described by the work of several well-known groups of researchers. Hybrid Dynamical Systems presents theoretical advances in such areas as diagnosability, observability and stabilization for various classes of system. Continuous and discrete state estimation and self-triggering control of nonlinear systems are advanced. The text employs various methods, among them, high-order sliding modes, Takagi–Sugeno representation and sampled-data switching to achieve its ends. The many applications of hybrid systems from power converters to computer science are not forgotten; studies of flexible-joint robotic arms and – as representative biological systems – the behaviour of the human heart and vasculature, demonstrate the wide-ranging practical significance of control in hybrid systems. The cross-disciplinary origins of study ...
Evolutionary design of discrete controllers for hybrid mechatronic systems
DEFF Research Database (Denmark)
Dupuis, Jean-Francois; Fan, Zhun; Goodman, Erik
2015-01-01
This paper investigates the issue of evolutionary design of controllers for hybrid mechatronic systems. Finite State Automaton (FSA) is selected as the representation for a discrete controller due to its interpretability, fast execution speed and natural extension to a statechart, which is very...... popular in industrial applications. A case study of a two-tank system is used to demonstrate that the proposed evolutionary approach can lead to a successful design of an FSA controller for the hybrid mechatronic system, represented by a hybrid bond graph. Generalisation of the evolved FSA controller...... of the evolutionary design of controllers for hybrid mechatronic systems. Finally, some important future research directions are pointed out, leading to the major work of the succeeding part of the research....
Nuclear facility safeguards systems modeling using discrete event simulation
International Nuclear Information System (INIS)
Engi, D.
1977-01-01
The threat of theft or dispersal of special nuclear material at a nuclear facility is treated by studying the temporal relationships between adversaries having authorized access to the facility (insiders) and safeguards system events by using a GASP IV discrete event simulation. The safeguards system events--detection, assessment, delay, communications, and neutralization--are modeled for the general insider adversary strategy which includes degradation of the safeguards system elements followed by an attempt to steal or disperse special nuclear material. The performance measure used in the analysis is the estimated probability of safeguards system success in countering the adversary based upon a predetermined set of adversary actions. An exemplary problem which includes generated results is presented for a hypothetical nuclear facility. The results illustrate representative information that could be utilized by safeguards decision-makers
Optimal reduction of flexible dynamic system
International Nuclear Information System (INIS)
Jankovic, J.
1994-01-01
Dynamic system reduction is basic procedure in various problems of active control synthesis of flexible structures. In this paper is presented direct method for system reduction by explicit extraction of modes included in reduced model form. Criterion for optimal system discrete approximation in synthesis reduced dynamic model is also presented. Subjected method of system decomposition is discussed in relation to the Schur method of solving matrix algebraic Riccati equation as condition for system reduction. By using exposed method procedure of flexible system reduction in addition with corresponding example is presented. Shown procedure is powerful in problems of active control synthesis of flexible system vibrations
Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain
Directory of Open Access Journals (Sweden)
Victor Kravets
2016-05-01
Full Text Available Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.
Directory of Open Access Journals (Sweden)
Yueyang Li
2014-01-01
Full Text Available This paper investigates the H∞ fixed-lag fault estimator design for linear discrete time-varying (LDTV systems with intermittent measurements, which is described by a Bernoulli distributed random variable. Through constructing a novel partially equivalent dynamic system, the fault estimator design is converted into a deterministic quadratic minimization problem. By applying the innovation reorganization technique and the projection formula in Krein space, a necessary and sufficient condition is obtained for the existence of the estimator. The parameter matrices of the estimator are derived by recursively solving two standard Riccati equations. An illustrative example is provided to show the effectiveness and applicability of the proposed algorithm.
Energy Technology Data Exchange (ETDEWEB)
Jankovsky, Zachary Kyle [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Denman, Matthew R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-05-01
It is difficult to assess the consequences of a transient in a sodium-cooled fast reactor (SFR) using traditional probabilistic risk assessment (PRA) methods, as numerous safety-related sys- tems have passive characteristics. Often there is significant dependence on the value of con- tinuous stochastic parameters rather than binary success/failure determinations. One form of dynamic PRA uses a system simulator to represent the progression of a transient, tracking events through time in a discrete dynamic event tree (DDET). In order to function in a DDET environment, a simulator must have characteristics that make it amenable to changing physical parameters midway through the analysis. The SAS4A SFR system analysis code did not have these characteristics as received. This report describes the code modifications made to allow dynamic operation as well as the linking to a Sandia DDET driver code. A test case is briefly described to demonstrate the utility of the changes.
International Nuclear Information System (INIS)
More, Ameya; Dutta, B.K.; Durgaprasad, P.V.; Arya, A.K.
2012-01-01
Fe-Cr based Ferritic/Martensitic (F/M) steels are the candidate structural materials for future fusion reactors. In this work, a multi-scale approach comprising atomistic Molecular Dynamics (MD) simulations and Discrete Dislocation Dynamics (DDD) simulations are used to model the effect of irradiation dose on the flow stress of F/M steels. At the atomic scale, molecular dynamics simulations are used to study the dislocation interaction with irradiation induced defects, i.e. voids and He bubbles. Whereas, the DDD simulations are used to estimate the change in flow stress of the material as a result of irradiation hardening. (author)
On various integrable discretizations of a general two-component Volterra system
International Nuclear Information System (INIS)
Babalic, Corina N; Carstea, A S
2013-01-01
We present two integrable discretizations of a general differential–difference bicomponent Volterra system. The results are obtained by discretizing directly the corresponding Hirota bilinear equations in two different ways. Multisoliton solutions are presented together with a new discrete form of Lotka–Volterra equation obtained by an alternative bilinearization. (paper)
Discrete Painlevé equations from Y-systems
International Nuclear Information System (INIS)
Hone, Andrew N W; Inoue, Rei
2014-01-01
We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlevé equations can arise from this construction. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
Functional envelope of a non-autonomous discrete system
Directory of Open Access Journals (Sweden)
Barzanouni Ali
2017-11-01
Full Text Available Let (X, F = {fn}n =0∞ be a non-autonomous discrete system by a compact metric space X and continuous maps fn : X → X, n = 0, 1, ....We introduce functional envelope (S(X, G = {Gn}n =0∞, of (X, F = {fn}n =0∞, where S(X is the space of all continuous self maps of X and the map Gn : S(X → S(X is defined by Gn(ϕ = Fn ∘ ϕ, Fn = fn ∘ fn-1 ∘ . . . ∘ f1 ∘ f0. The paper mainly deals with the connection between the properties of a system and the properties of its functional envelope.
3D Discrete Dislocation Dynamics: Influence of Segment Mobility on Critical Shear Stress
Czech Academy of Sciences Publication Activity Database
Záležák, Tomáš; Dlouhý, Antonín
2015-01-01
Roč. 128, č. 4 (2015), s. 654-656 ISSN 0587-4246. [ISPMA 13 - International Symposium on Physics of Materials /13./. Praha, 31.08.2014-04.09.2014] R&D Projects: GA MŠk(CZ) EE2.3.20.0214; GA ČR(CZ) GA14-22834S Institutional support: RVO:68081723 Keywords : metal matrix composites * discrete dislocation dynamics * high temperature creep Subject RIV: JG - Metallurgy Impact factor: 0.525, year: 2015
Zeng, Cheng; Liang, Shan; Xiang, Shuwen
2017-05-01
Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Pilyugin, Sergei Yu
2012-01-01
Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion.In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories are covered, as well as nonlinearity. The author is an experienced book writer and his work is based on years of teaching.
Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games.
Wei, Qinglai; Liu, Derong; Lin, Qiao; Song, Ruizhuo
2018-04-01
In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.
Discrete dynamic event tree modeling and analysis of nuclear power plant crews for safety assessment
International Nuclear Information System (INIS)
Mercurio, D.
2011-01-01
Current Probabilistic Risk Assessment (PRA) and Human Reliability Analysis (HRA) methodologies model the evolution of accident sequences in Nuclear Power Plants (NPPs) mainly based on Logic Trees. The evolution of these sequences is a result of the interactions between the crew and plant; in current PRA methodologies, simplified models of these complex interactions are used. In this study, the Accident Dynamic Simulator (ADS), a modeling framework based on the Discrete Dynamic Event Tree (DDET), has been used for the simulation of crew-plant interactions during potential accident scenarios in NPPs. In addition, an operator/crew model has been developed to treat the response of the crew to the plant. The 'crew model' is made up of three operators whose behavior is guided by a set of rules-of-behavior (which represents the knowledge and training of the operators) coupled with written and mental procedures. In addition, an approach for addressing the crew timing variability in DDETs has been developed and implemented based on a set of HRA data from a simulator study. Finally, grouping techniques were developed and applied to the analysis of the scenarios generated by the crew-plant simulation. These techniques support the post-simulation analysis by grouping similar accident sequences, identifying the key contributing events, and quantifying the conditional probability of the groups. These techniques are used to characterize the context of the crew actions in order to obtain insights for HRA. The model has been applied for the analysis of a Small Loss Of Coolant Accident (SLOCA) event for a Pressurized Water Reactor (PWR). The simulation results support an improved characterization of the performance conditions or context of operator actions, which can be used in an HRA, in the analysis of the reliability of the actions. By providing information on the evolution of system indications, dynamic of cues, crew timing in performing procedure steps, situation
Defense Strategies for Asymmetric Networked Systems with Discrete Components
Directory of Open Access Journals (Sweden)
Nageswara S. V. Rao
2018-05-01
Full Text Available We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.
Defense Strategies for Asymmetric Networked Systems with Discrete Components.
Rao, Nageswara S V; Ma, Chris Y T; Hausken, Kjell; He, Fei; Yau, David K Y; Zhuang, Jun
2018-05-03
We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
Gils, S; Hoveijn, I; Takens, F; Nonlinear Dynamical Systems and Chaos
1996-01-01
Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
The effects of host-feeding on stability of discrete-time host-parasitoid population dynamic models.
Emerick, Brooks; Singh, Abhyudai
2016-02-01
Discrete-time models are the traditional approach for capturing population dynamics of a host-parasitoid system. Recent work has introduced a semi-discrete framework for obtaining model update functions that connect host-parasitoid population levels from year-to-year. In particular, this framework uses differential equations to describe the host-parasitoid interaction during the time of year when they come in contact, allowing specific behaviors to be mechanistically incorporated. We use the semi-discrete approach to study the effects of host-feeding, which occurs when a parasitoid consumes a potential host larva without ovipositing. We find that host-feeding by itself cannot stabilize the system, and both populations exhibit behavior similar to the Nicholson-Bailey model. However, when combined with stabilizing mechanisms such as density-dependent host mortality, host-feeding contracts the region of parameter space that allows for a stable host-parasitoid equilibrium. In contrast, when combined with a density-dependent parasitoid attack rate, host-feeding expands the non-zero equilibrium stability region. Our results show that host-feeding causes inefficiency in the parasitoid population, which yields a higher population of hosts per generation. This suggests that host-feeding may have limited long-term impact in terms of suppressing host levels for biological control applications. Copyright © 2015 Elsevier Inc. All rights reserved.
Bengoetxea, Ana; Leurs, Françoise; Hoellinger, Thomas; Cebolla, Ana M; Dan, Bernard; McIntyre, Joseph; Cheron, Guy
2014-01-01
In this study we employed a dynamic recurrent neural network (DRNN) in a novel fashion to reveal characteristics of control modules underlying the generation of muscle activations when drawing figures with the outstretched arm. We asked healthy human subjects to perform four different figure-eight movements in each of two workspaces (frontal plane and sagittal plane). We then trained a DRNN to predict the movement of the wrist from information in the EMG signals from seven different muscles. We trained different instances of the same network on a single movement direction, on all four movement directions in a single movement plane, or on all eight possible movement patterns and looked at the ability of the DRNN to generalize and predict movements for trials that were not included in the training set. Within a single movement plane, a DRNN trained on one movement direction was not able to predict movements of the hand for trials in the other three directions, but a DRNN trained simultaneously on all four movement directions could generalize across movement directions within the same plane. Similarly, the DRNN was able to reproduce the kinematics of the hand for both movement planes, but only if it was trained on examples performed in each one. As we will discuss, these results indicate that there are important dynamical constraints on the mapping of EMG to hand movement that depend on both the time sequence of the movement and on the anatomical constraints of the musculoskeletal system. In a second step, we injected EMG signals constructed from different synergies derived by the PCA in order to identify the mechanical significance of each of these components. From these results, one can surmise that discrete-rhythmic movements may be constructed from three different fundamental modules, one regulating the co-activation of all muscles over the time span of the movement and two others elliciting patterns of reciprocal activation operating in orthogonal directions.
Dynamical systems on 2- and 3-manifolds
Grines, Viacheslav Z; Pochinka, Olga V
2016-01-01
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are present...
Dynamic Optimization of a Polymer Flooding Process Based on Implicit Discrete Maximum Principle
Directory of Open Access Journals (Sweden)
Yang Lei
2012-01-01
Full Text Available Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR. In this paper, an optimal control model of distributed parameter systems (DPSs for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and some inequality constraints as polymer concentration and injection amount limitation. The optimal control model is discretized by full implicit finite-difference method. To cope with the discrete optimal control problem (OCP, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s discrete maximum principle. A modified gradient method with new adjoint construction is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.
Discrete Event Supervisory Control Applied to Propulsion Systems
Litt, Jonathan S.; Shah, Neerav
2005-01-01
The theory of discrete event supervisory (DES) control was applied to the optimal control of a twin-engine aircraft propulsion system and demonstrated in a simulation. The supervisory control, which is implemented as a finite-state automaton, oversees the behavior of a system and manages it in such a way that it maximizes a performance criterion, similar to a traditional optimal control problem. DES controllers can be nested such that a high-level controller supervises multiple lower level controllers. This structure can be expanded to control huge, complex systems, providing optimal performance and increasing autonomy with each additional level. The DES control strategy for propulsion systems was validated using a distributed testbed consisting of multiple computers--each representing a module of the overall propulsion system--to simulate real-time hardware-in-the-loop testing. In the first experiment, DES control was applied to the operation of a nonlinear simulation of a turbofan engine (running in closed loop using its own feedback controller) to minimize engine structural damage caused by a combination of thermal and structural loads. This enables increased on-wing time for the engine through better management of the engine-component life usage. Thus, the engine-level DES acts as a life-extending controller through its interaction with and manipulation of the engine s operation.
National Research Council Canada - National Science Library
Ng, Chee W
2007-01-01
.... Discrete-event simulation (DES) was used to simulate a typical port-security, local, waterside-threat response model and to test the adaptive response of asymmetric threats in reaction to port-security procedures, while a multi-agent system (MAS...
Discrete kink dynamics in hydrogen-bonded chains: The one-component model
DEFF Research Database (Denmark)
Karpan, V. M.; Zolotaryuk, Yaroslav; Christiansen, Peter Leth
2002-01-01
"parabola-constant" approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete traveling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity...
Directory of Open Access Journals (Sweden)
Saïda Bedoui
2013-01-01
Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.
International Nuclear Information System (INIS)
Yu Fajun
2008-01-01
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)], E-mail: yufajun888@163.com
2008-06-09
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity.
Switched periodic systems in discrete time: stability and input-output norms
Bolzern, Paolo; Colaneri, Patrizio
2013-07-01
This paper deals with the analysis of stability and the characterisation of input-output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H2 and H∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
Discrete Adjoint-Based Design for Unsteady Turbulent Flows On Dynamic Overset Unstructured Grids
Nielsen, Eric J.; Diskin, Boris
2012-01-01
A discrete adjoint-based design methodology for unsteady turbulent flows on three-dimensional dynamic overset unstructured grids is formulated, implemented, and verified. The methodology supports both compressible and incompressible flows and is amenable to massively parallel computing environments. The approach provides a general framework for performing highly efficient and discretely consistent sensitivity analysis for problems involving arbitrary combinations of overset unstructured grids which may be static, undergoing rigid or deforming motions, or any combination thereof. General parent-child motions are also accommodated, and the accuracy of the implementation is established using an independent verification based on a complex-variable approach. The methodology is used to demonstrate aerodynamic optimizations of a wind turbine geometry, a biologically-inspired flapping wing, and a complex helicopter configuration subject to trimming constraints. The objective function for each problem is successfully reduced and all specified constraints are satisfied.
Periodic Properties of 1D FE Discrete Models in High Frequency Dynamics
Directory of Open Access Journals (Sweden)
A. Żak
2016-01-01
Full Text Available Finite element discrete models of various engineering 1D structures may be considered as structures of certain periodic characteristics. The source of this periodicity comes from the discontinuity of stress/strain field between the elements. This behaviour remains unnoticeable, when low frequency dynamics of these structures is investigated. At high frequency regimes, however, its influence may be strong enough to dominate calculated structural responses distorting or even falsifying them completely. In this paper, certain computational aspects of structural periodicity of 1D FE discrete models are discussed by the authors. In this discussion, the authors focus their attention on an exemplary problem of 1D rod modelled according to the elementary theory.
2014-01-01
Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP), which aims to minimize total service time, and proposes an iterated greedy (IG) algorithm to solve it. The proposed IG algorithm is tested on three benchmark problem sets. Experimental results show that the proposed IG algorithm can obtain optimal solutions for all test instances of the first and second problem sets and outperforms the best-known solutions for 35 out of 90 test instances of the third problem set. PMID:25295295
Directory of Open Access Journals (Sweden)
Shih-Wei Lin
2014-01-01
Full Text Available Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP, which aims to minimize total service time, and proposes an iterated greedy (IG algorithm to solve it. The proposed IG algorithm is tested on three benchmark problem sets. Experimental results show that the proposed IG algorithm can obtain optimal solutions for all test instances of the first and second problem sets and outperforms the best-known solutions for 35 out of 90 test instances of the third problem set.
Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems
Srinivasan, K.; Raghavan, G.
2018-03-01
Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.
State-feedback control of fuzzy discrete-event systems.
Lin, Feng; Ying, Hao
2010-06-01
In a 2002 paper, we combined fuzzy logic with discrete-event systems (DESs) and established an automaton model of fuzzy DESs (FDESs). The model can effectively represent deterministic uncertainties and vagueness, as well as human subjective observation and judgment inherent to many real-world problems, particularly those in biomedicine. We also investigated optimal control of FDESs and applied the results to optimize HIV/AIDS treatments for individual patients. Since then, other researchers have investigated supervisory control problems in FDESs, and several results have been obtained. These results are mostly derived by extending the traditional supervisory control of (crisp) DESs, which are string based. In this paper, we develop state-feedback control of FDESs that is different from the supervisory control extensions. We use state space to describe the system behaviors and use state feedback in control. Both disablement and enforcement are allowed. Furthermore, we study controllability based on the state space and prove that a controller exists if and only if the controlled system behavior is (state-based) controllable. We discuss various properties of the state-based controllability. Aside from novelty, the proposed new framework has the advantages of being able to address a wide range of practical problems that cannot be effectively dealt with by existing approaches. We use the diabetes treatment as an example to illustrate some key aspects of our theoretical results.
Synchronous Parallel System for Emulation and Discrete Event Simulation
Steinman, Jeffrey S. (Inventor)
2001-01-01
A synchronous parallel system for emulation and discrete event simulation having parallel nodes responds to received messages at each node by generating event objects having individual time stamps, stores only the changes to the state variables of the simulation object attributable to the event object and produces corresponding messages. The system refrains from transmitting the messages and changing the state variables while it determines whether the changes are superseded, and then stores the unchanged state variables in the event object for later restoral to the simulation object if called for. This determination preferably includes sensing the time stamp of each new event object and determining which new event object has the earliest time stamp as the local event horizon, determining the earliest local event horizon of the nodes as the global event horizon, and ignoring events whose time stamps are less than the global event horizon. Host processing between the system and external terminals enables such a terminal to query, monitor, command or participate with a simulation object during the simulation process.
Compositionality issues in discrete, continuous and hybrid systems
van der Schaft, Arjan; Schumacher, J.M.
2000-01-01
Models of complex dynamical systems are often built by connecting submodels of smaller parts. The key to this method is the operation of ``interconnection'' or ``composition'' which serves to define the whole in terms of its parts. In the setting of smooth differential equations the composition
International Nuclear Information System (INIS)
Shin, Seung Ki; Seong, Poong Hyun
2008-01-01
Conventional static reliability analysis methods are inadequate for modeling dynamic interactions between components of a system. Various techniques such as dynamic fault tree, dynamic Bayesian networks, and dynamic reliability block diagrams have been proposed for modeling dynamic systems based on improvement of the conventional modeling methods. In this paper, we review these methods briefly and introduce dynamic nodes to the existing Reliability Graph with General Gates (RGGG) as an intuitive modeling method to model dynamic systems. For a quantitative analysis, we use a discrete-time method to convert an RGGG to an equivalent Bayesian network and develop a software tool for generation of probability tables
Energy conservation in molecular dynamics simulations of classical systems
DEFF Research Database (Denmark)
Toxværd, Søren; Heilmann, Ole; Dyre, J. C.
2012-01-01
Classical Newtonian dynamics is analytic and the energy of an isolated system is conserved. The energy of such a system, obtained by the discrete “Verlet” algorithm commonly used in molecular dynamics simulations, fluctuates but is conserved in the mean. This is explained by the existence...
Dynamic Systems and Control Engineering
International Nuclear Information System (INIS)
Kim, Jong Seok
1994-02-01
This book deals with introduction of dynamic system and control engineering, frequency domain modeling of dynamic system, temporal modeling of dynamic system, typical dynamic system and automatic control device, performance and stability of control system, root locus analysis, analysis of frequency domain dynamic system, design of frequency domain dynamic system, design and analysis of space, space of control system and digital control system such as control system design of direct digital and digitalization of consecutive control system.
Dynamic Systems and Control Engineering
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Seok
1994-02-15
This book deals with introduction of dynamic system and control engineering, frequency domain modeling of dynamic system, temporal modeling of dynamic system, typical dynamic system and automatic control device, performance and stability of control system, root locus analysis, analysis of frequency domain dynamic system, design of frequency domain dynamic system, design and analysis of space, space of control system and digital control system such as control system design of direct digital and digitalization of consecutive control system.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Observability of discretized partial differential equations
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
Stability of dynamical systems
Liao, Xiaoxin; Yu, P 0
2007-01-01
The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.ʺ Presents
A non-linear discrete transform for pattern recognition of discrete chaotic systems
International Nuclear Information System (INIS)
Karanikas, C.; Proios, G.
2003-01-01
It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter
A non-linear discrete transform for pattern recognition of discrete chaotic systems
Karanikas, C
2003-01-01
It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.
uncertain dynamic systems on time scales
Directory of Open Access Journals (Sweden)
V. Lakshmikantham
1995-01-01
Full Text Available A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.
Dynamical Properties of Discrete-Time Background Neural Networks with Uniform Firing Rate
Directory of Open Access Journals (Sweden)
Min Wan
2013-01-01
Full Text Available The dynamics of a discrete-time background network with uniform firing rate and background input is investigated. The conditions for stability are firstly derived. An invariant set is then obtained so that the nondivergence of the network can be guaranteed. In the invariant set, it is proved that all trajectories of the network starting from any nonnegative value will converge to a fixed point under some conditions. In addition, bifurcation and chaos are discussed. It is shown that the network can engender bifurcation and chaos with the increase of background input. The computations of Lyapunov exponents confirm the chaotic behaviors.
3D Discrete Dislocation Dynamics Applied to Interactions between Dislocation Walls and Particles
Czech Academy of Sciences Publication Activity Database
Záležák, Tomáš; Dlouhý, Antonín
2012-01-01
Roč. 122, č. 3 (2012), s. 450-452 ISSN 0587-4246. [International Symposium on Physics of Materials /12./ - ISPMA 12. Prague, 04.09.2011-08.09.2011] R&D Projects: GA ČR GD106/09/H035; GA ČR GA202/09/2073; GA MŠk OC 162 Institutional research plan: CEZ:AV0Z20410507 Keywords : 3D discrete dislocation dynamics * tilt boundary * migration * diffusion * pecipitation hardening Subject RIV: JG - Metallurgy Impact factor: 0.531, year: 2012
Recent Progress in Discrete Dislocation Dynamics and Its Applications to Micro Plasticity
Po, Giacomo; Mohamed, Mamdouh S.; Crosby, Tamer; Erel, Can; El-Azab, Anter; Ghoniem, Nasr
2014-01-01
We present a self-contained review of the discrete dislocation dynamics (DDD) method for the numerical investigation of plasticity in crystals, focusing on recent development and implementation progress. The review covers the theoretical foundations of DDD within the framework of incompatible elasticity, its numerical implementation via the nodal method, the extension of the method to finite domains and several implementation details. Applications of the method to current topics in micro-plasticity are presented, including the size effects in nano-indentation, the evolution of the dislocation microstructure in persistent slip bands, and the phenomenon of dislocation avalanches in micro-pillar compression.
International Nuclear Information System (INIS)
Bertolino, G.; Sauzay, M.; Bertolino, G.; Doquet, V.
2003-01-01
An attempt to model the variability of short cracks development in high-cycle fatigue is made by coupling finite element calculations of the stresses ahead of a microcrack in a polycrystal with simulations of crack growth along slip planes based on discrete dislocations dynamics. The model predicts a large scatter in growth rates related to the roughness of the crack path. It also describes the influence of the mean grain size and the fact that overloads may suppress the endurance limit by allowing arrested cracks to cross the grain boundaries. (authors)
Directory of Open Access Journals (Sweden)
Lešinskis Aloizs
2017-08-01
Full Text Available Aircraft crew training corresponds to the interactive learning models of sensorimotor skill acquisition, and the dynamics of skill acquirement can be approximated by the exponential trend. A model of 5-grade assessment of separate exercises is offered. It helps to calculate a resulting evaluation, in accordance with which the progress level of a discrete exercise is evaluated. Such an evaluation forms one of the points for the analytical construction of a learning curve using the Gaussian method. Possible applications of the learning curve are covered.
Recent Progress in Discrete Dislocation Dynamics and Its Applications to Micro Plasticity
Po, Giacomo
2014-09-27
We present a self-contained review of the discrete dislocation dynamics (DDD) method for the numerical investigation of plasticity in crystals, focusing on recent development and implementation progress. The review covers the theoretical foundations of DDD within the framework of incompatible elasticity, its numerical implementation via the nodal method, the extension of the method to finite domains and several implementation details. Applications of the method to current topics in micro-plasticity are presented, including the size effects in nano-indentation, the evolution of the dislocation microstructure in persistent slip bands, and the phenomenon of dislocation avalanches in micro-pillar compression.
Dynamics of a discrete geotropic sensor subject to rotation-induced gravity compensation
Energy Technology Data Exchange (ETDEWEB)
Silver, I.L.
1976-01-01
A clinostat achieves gravity compensation by providing circular rotation with uniform speed, about a horizontal axis. The dynamics of an assumed, discrete and free-moving subcellular gravity receptor, subject to clinostat rotation, is analyzed. The results imply that there is an optimum rotation rate; higher speeds result in circular motions with diameters more comparable to thermal noise fluctuations, but with greater linear velocities due to increasing centrifugal forces. An optimizing function is proposed. The nucleolus and mitochondrion is chosen as a gravity receptor for illustrating the use of this theory. The characteristics of their clinostat-induced motions are incorporated with experimental results on Avena plant shoots in an illustrative example.
Fractional equations of kicked systems and discrete maps
International Nuclear Information System (INIS)
Tarasov, Vasily E; Zaslavsky, George M
2008-01-01
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain 'fractional' discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main property of the suggested fractional maps is a long-term memory. The memory effects in the fractional discrete maps mean that their present state evolution depends on all past states with special forms of weights. These forms are represented by combinations of power-law functions
Institute of Scientific and Technical Information of China (English)
Jian-Yong Zhang; Li-Hua Zeng; Juan Feng
2017-01-01
Dynamic covalent chemistry has emerged recently to be a powerful tool to construct functional materials.This article reviews the progress in the research and development of dynamic covalent chemistry in gels assembled from small molecules.First dynamic covalent reactions used in gels are reviewed to understand the dynamic covalent bonding.Afterwards the catalogues of dynamic covalent gels are reviewed according to the nature of gelators and the interactions between gelators.Dynamic covalent bonding can be involved to form low molecular weight gelators.Low molecular weight molecules with multiple functional groups react to form dynamic covalent cross-linked polymers and act as gelators.Two catalogues of gels show different properties arising from their different structures.This review aims to illustrate the structure-property relationships of these dynamic covalent gels.
International Nuclear Information System (INIS)
Posch, H.A.; Narnhofer, H.; Thirring, W.
1990-01-01
We study the dynamics of classical particles interacting with attractive Gaussian potentials. This system is thermodynamically not stable and exhibits negative specific heat. The results of the computer simulation of the dynamics are discussed in comparison with various theories. In particular, we find that the condensed phase is a stationary solution of the Vlasov equation, but the Vlasov dynamics cannot describe the collapse. 14 refs., 1 tab., 11 figs. (Authors)
Ligterink, N.E.
2007-01-01
Functional system dynamics is the analysis, modelling, and simulation of continuous systems usually described by partial differential equations. From the infinite degrees of freedom of such systems only a finite number of relevant variables have to be chosen for a practical model description. The proper input and output of the system are an important part of the relevant variables.
Control of discrete-event systems with modular or distributed structure
Czech Academy of Sciences Publication Activity Database
Komenda, Jan; van Schuppen, J. H.
2007-01-01
Roč. 388, č. 3 (2007), s. 199-226 ISSN 0304-3975 R&D Projects: GA AV ČR(CZ) KJB100190609 Institutional research plan: CEZ:AV0Z10190503 Keywords : supervisory control * modular discrete-event system * distributed discrete-event system Subject RIV: BA - General Mathematics Impact factor: 0.735, year: 2007
Shadowing in dynamical systems
Pilyugin, Sergei Yu
1999-01-01
This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
International Nuclear Information System (INIS)
Doebrich, Marcus; Markstaller, Klaus; Karmrodt, Jens; Kauczor, Hans-Ulrich; Eberle, Balthasar; Weiler, Norbert; Thelen, Manfred; Schreiber, Wolfgang G
2005-01-01
In this study, an algorithm was developed to measure the distribution of pulmonary time constants (TCs) from dynamic computed tomography (CT) data sets during a sudden airway pressure step up. Simulations with synthetic data were performed to test the methodology as well as the influence of experimental noise. Furthermore the algorithm was applied to in vivo data. In five pigs sudden changes in airway pressure were imposed during dynamic CT acquisition in healthy lungs and in a saline lavage ARDS model. The fractional gas content in the imaged slice (FGC) was calculated by density measurements for each CT image. Temporal variations of the FGC were analysed assuming a model with a continuous distribution of exponentially decaying time constants. The simulations proved the feasibility of the method. The influence of experimental noise could be well evaluated. Analysis of the in vivo data showed that in healthy lungs ventilation processes can be more likely characterized by discrete TCs whereas in ARDS lungs continuous distributions of TCs are observed. The temporal behaviour of lung inflation and deflation can be characterized objectively using the described new methodology. This study indicates that continuous distributions of TCs reflect lung ventilation mechanics more accurately compared to discrete TCs
Invitation to dynamical systems
Scheinerman, Edward R
2012-01-01
This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...... of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped...... narrow spikes. The influence of the point impurities on this dynamics is also investigated....
Zhang, Huaguang; Jiang, He; Luo, Chaomin; Xiao, Geyang
2017-10-01
In this paper, we investigate the nonzero-sum games for a class of discrete-time (DT) nonlinear systems by using a novel policy iteration (PI) adaptive dynamic programming (ADP) method. The main idea of our proposed PI scheme is to utilize the iterative ADP algorithm to obtain the iterative control policies, which not only ensure the system to achieve stability but also minimize the performance index function for each player. This paper integrates game theory, optimal control theory, and reinforcement learning technique to formulate and handle the DT nonzero-sum games for multiplayer. First, we design three actor-critic algorithms, an offline one and two online ones, for the PI scheme. Subsequently, neural networks are employed to implement these algorithms and the corresponding stability analysis is also provided via the Lyapunov theory. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.
Discrete-event system simulation on small and medium enterprises productivity improvement
Sulistio, J.; Hidayah, N. A.
2017-12-01
Small and medium industries in Indonesia is currently developing. The problem faced by SMEs is the difficulty of meeting growing demand coming into the company. Therefore, SME need an analysis and evaluation on its production process in order to meet all orders. The purpose of this research is to increase the productivity of SMEs production floor by applying discrete-event system simulation. This method preferred because it can solve complex problems die to the dynamic and stochastic nature of the system. To increase the credibility of the simulation, model validated by cooperating the average of two trials, two trials of variance and chi square test. Afterwards, Benferroni method applied to development several alternatives. The article concludes that, the productivity of SMEs production floor increased up to 50% by adding the capacity of dyeing and drying machines.
LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.
Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong
2017-03-01
In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.
Ligterink, N.E.
2007-01-01
Functional system dynamics is the analysis, modelling, and simulation of continuous systems usually described by partial differential equations. From the infinite degrees of freedom of such systems only a finite number of relevant variables have to be chosen for a practical model description. The
Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.
Kiumarsi, Bahare; Lewis, Frank L
2015-01-01
This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Time Span of Discretion and Administrative Work in School Systems: Results of a Pilot Study.
Allison, Derek J.; Morfitt, Grace
This paper presents findings of a study that utilized Elliott Jaques' theories of organizational depth structure and time span of discretion in administrative work to examine administrators' responsibilities in two Ontario (Canada) school systems. The theory predicts that the time-span of discretion associated with the administrative tasks will…
A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics
Powers, Robert A.; Allison, Dean E.; Grassl, Richard M.
2005-01-01
This study investigated the impact of the TI-92 handheld Computer Algebra System (CAS) on student achievement in a discrete mathematics course. Specifically, the researchers examined the differences between a CAS section and a control section of discrete mathematics on students' in-class examinations. Additionally, they analysed student approaches…
Improving the Teaching of Discrete-Event Control Systems Using a LEGO Manufacturing Prototype
Sanchez, A.; Bucio, J.
2012-01-01
This paper discusses the usefulness of employing LEGO as a teaching-learning aid in a post-graduate-level first course on the control of discrete-event systems (DESs). The final assignment of the course is presented, which asks students to design and implement a modular hierarchical discrete-event supervisor for the coordination layer of a…
Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems
Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri
2018-05-01
The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.
Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion
International Nuclear Information System (INIS)
Garrido-Atienza, Maria J.; Kloeden, Peter E.; Neuenkirch, Andreas
2009-01-01
In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases
Dynamics of Information Systems
Hirsch, Michael J; Murphey, Robert
2010-01-01
Our understanding of information and information dynamics has outgrown classical information theory. This book presents the research explaining the importance of information in the evolution of a distributed or networked system. It presents techniques for measuring the value or significance of information within the context of a system
DEFF Research Database (Denmark)
Lashab, Abderezak; Sera, Dezso; Guerrero, Josep M.
2018-01-01
The main objective of this work is to provide an overview and evaluation of discrete model predictive controlbased maximum power point tracking (MPPT) for PV systems. A large number of MPC based MPPT methods have been recently introduced in the literature with very promising performance, however......, an in-depth investigation and comparison of these methods have not been carried out yet. Therefore, this paper has set out to provide an in-depth analysis and evaluation of MPC based MPPT methods applied to various common power converter topologies. The performance of MPC based MPPT is directly linked...... with the converter topology, and it is also affected by the accurate determination of the converter parameters, sensitivity to converter parameter variations is also investigated. The static and dynamic performance of the trackers are assessed according to the EN 50530 standard, using detailed simulation models...
Transformation of nonlinear discrete-time system into the extended observer form
Kaparin, V.; Kotta, Ü.
2018-04-01
The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input-output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.
A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system
International Nuclear Information System (INIS)
Zhao, Hai-qiong; Yuan, Jinyun
2016-01-01
A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N -fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit. (paper)
Directory of Open Access Journals (Sweden)
Roman Senkerik
2014-01-01
Full Text Available Evolutionary technique differential evolution (DE is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.
A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications
Directory of Open Access Journals (Sweden)
Mei Zhang
2015-01-01
Full Text Available Firstly, this study introduces a definition of generalized stability (GST in discrete-time nonautonomous chaos system (DNCS, which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.
Paul, Rimi; Sengupta, Anindita
2017-11-01
A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. This controller generates control signal using node coefficients of the error signal which interprets many implicit phenomena such as process dynamics, measurement noise and effect of external disturbances. Through simulation results on LLS problem, this controller is shown to perform faster than both the discrete wavelet transform based controller and conventional proportional integral controller. Also, it is more efficient in terms of its ability to provide better noise rejection. To overcome the wind up phenomenon by considering the saturation due to presence of actuator, anti-wind up technique is applied to the conventional PI controller and compared to the wavelet packet transform based controller. In this case also, packet controller is found better than the other ones. This similar work has been extended for analogous first order RC plant as well as second order plant also. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Anak Agung Julius, A.A.J.; van der Schaft, Arjan
2004-01-01
In this paper we formulate a general framework based on the behavioral approach to dynamical systems, in which various issues regarding interconnection of systems can be addressed. The main part of the framework is that interconnections or compositions of systems can be modelled with interconnection
International Nuclear Information System (INIS)
Cugliandolo, Leticia F.
2003-09-01
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario for this temporal evolution derived from the solution to some solvable models (p spin and the like) that are intimately connected to the mode coupling approach (and similar ones) to super-cooled liquids. At the end we list a number of open problems of great relevance in this context. These Sections can be read independently of the body of the paper where we present some of the basic analytic techniques used to study the out of equilibrium dynamics of classical and quantum models with and without disorder. We start the technical part by briefly discussing the role played by the environment and by introducing and comparing its representation in the equilibrium and dynamic treatment of classical and quantum systems. We next explain the role played by explicit quenched disorder in both approaches. Later on we focus on analytical techniques; we expand on the dynamic functional methods, and the diagrammatic expansions and resummations used to derive macroscopic equations from the microscopic dynamics. We show why the macroscopic dynamic equations for disordered models and those resulting from self-consistent approximations to non-disordered ones coincide. We review some generic properties of dynamic systems evolving out of equilibrium like the modifications of the fluctuation-dissipation theorem, generic scaling forms of the correlation functions, etc. Finally we solve a family of mean-field models. The connection between the dynamic treatment and the analysis of the free-energy landscape of these models is also presented. We use pedagogical examples all along these lectures to illustrate the properties and results. (author)
Discrete coherent and squeezed states of many-qudit systems
International Nuclear Information System (INIS)
Klimov, Andrei B.; Munoz, Carlos; Sanchez-Soto, Luis L.
2009-01-01
We consider the phase space for n identical qudits (each one of dimension d, with d a primer number) as a grid of d n xd n points and use the finite Galois field GF(d n ) to label the corresponding axes. The associated displacement operators permit to define s-parametrized quasidistributions on this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states of different qudits.
Complexity in Dynamical Systems
Moore, Cristopher David
The study of chaos has shown us that deterministic systems can have a kind of unpredictability, based on a limited knowledge of their initial conditions; after a finite time, the motion appears essentially random. This observation has inspired a general interest in the subject of unpredictability, and more generally, complexity; how can we characterize how "complex" a dynamical system is?. In this thesis, we attempt to answer this question with a paradigm of complexity that comes from computer science, we extract sets of symbol sequences, or languages, from a dynamical system using standard methods of symbolic dynamics; we then ask what kinds of grammars or automata are needed a generate these languages. This places them in the Chomsky heirarchy, which in turn tells us something about how subtle and complex the dynamical system's behavior is. This gives us insight into the question of unpredictability, since these automata can also be thought of as computers attempting to predict the system. In the culmination of the thesis, we find a class of smooth, two-dimensional maps which are equivalent to the highest class in the Chomsky heirarchy, the turning machine; they are capable of universal computation. Therefore, these systems possess a kind of unpredictability qualitatively different from the usual "chaos": even if the initial conditions are known exactly, questions about the system's long-term dynamics are undecidable. No algorithm exists to answer them. Although this kind of unpredictability has been discussed in the context of distributed, many-degree-of -freedom systems (for instance, cellular automata) we believe this is the first example of such phenomena in a smooth, finite-degree-of-freedom system.
Directory of Open Access Journals (Sweden)
Guitao Zhang
2014-01-01
Full Text Available The advertisement can increase the consumers demand; therefore it is one of the most important marketing strategies in the operations management of enterprises. This paper aims to analyze the impact of advertising investment on a discrete dynamic supply chain network which consists of suppliers, manufactures, retailers, and demand markets associated at different tiers under random demand. The impact of advertising investment will last several planning periods besides the current period due to delay effect. Based on noncooperative game theory, variational inequality, and Lagrange dual theory, the optimal economic behaviors of the suppliers, the manufactures, the retailers, and the consumers in the demand markets are modeled. In turn, the supply chain network equilibrium model is proposed and computed by modified project contraction algorithm with fixed step. The effectiveness of the model is illustrated by numerical examples, and managerial insights are obtained through the analysis of advertising investment in multiple periods and advertising delay effect among different periods.
Czech Academy of Sciences Publication Activity Database
Záležák, Tomáš; Svoboda, Jiří; Dlouhý, Antonín
2017-01-01
Roč. 97, OCT (2017), s. 1-23 ISSN 0749-6419 R&D Projects: GA ČR(CZ) GA14-22834S; GA ČR(CZ) GA202/09/2073; GA ČR(CZ) GD106/09/H035; GA MŠk(CZ) EE2.3.20.0214; GA MŠk OC 162 EU Projects: European Commission(XE) 309916 - Z-ULTRA Institutional support: RVO:68081723 Keywords : 3D discrete dislocation dynamics * Dislocations * Strengthening mechanisms * Low angle grain boundaries * Particulate reinforced material Subject RIV: JI - Composite Materials OBOR OECD: Composites (including laminates, reinforced plastics, cermets, combined natural and synthetic fibre fabrics Impact factor: 5.702, year: 2016
Discrete systems related to the sixth Painleve equation
International Nuclear Information System (INIS)
Ramani, A; Ohta, Y; Grammaticos, B
2006-01-01
We present discrete Painleve equations which can be obtained as contiguity relations of the solutions of the continuous Painleve VI. The derivation is based on the geometry of the affine Weyl group D (1) 4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau-Ablowitz-Fokas equation, which is a Miura transformed, 'modified', P VI
Multisite Testing of the Discrete Address Beacon System (DABS).
1981-07-01
discrete address would the new DABS/ATCRBS environment, thus, allow individual interrogation of each allowing for an economical transition aircraft so...Traffic used. These changes were primarily Advisory and Resolution Service ( ATARS ) concerned with ATCRBS performance and function and ATC en route...the zenith cones and potential ATARS list of "assigned" sensors; i.e., those conflicts with the stationary Mizpah being used for redundant surveillance
Fundamental aspects of brittle damage processes -- discrete systems
International Nuclear Information System (INIS)
Krajcinovic, D.; Lubarda, V.
1993-01-01
The analysis of cooperative brittle processes are performed on simple discrete models admitting closed form solutions. A connection between the damage and fracture mechanics is derived and utilized to illustrate the relation between two theories. The performed analyses suggest that the stress concentrations (direct interaction between defects) represent a second order effect during the hardening part of the response in the case of disordered solids
A novel approach for modelling complex maintenance systems using discrete event simulation
International Nuclear Information System (INIS)
Alrabghi, Abdullah; Tiwari, Ashutosh
2016-01-01
Existing approaches for modelling maintenance rely on oversimplified assumptions which prevent them from reflecting the complexity found in industrial systems. In this paper, we propose a novel approach that enables the modelling of non-identical multi-unit systems without restrictive assumptions on the number of units or their maintenance characteristics. Modelling complex interactions between maintenance strategies and their effects on assets in the system is achieved by accessing event queues in Discrete Event Simulation (DES). The approach utilises the wide success DES has achieved in manufacturing by allowing integration with models that are closely related to maintenance such as production and spare parts systems. Additional advantages of using DES include rapid modelling and visual interactive simulation. The proposed approach is demonstrated in a simulation based optimisation study of a published case. The current research is one of the first to optimise maintenance strategies simultaneously with their parameters while considering production dynamics and spare parts management. The findings of this research provide insights for non-conflicting objectives in maintenance systems. In addition, the proposed approach can be used to facilitate the simulation and optimisation of industrial maintenance systems. - Highlights: • This research is one of the first to optimise maintenance strategies simultaneously. • New insights for non-conflicting objectives in maintenance systems. • The approach can be used to optimise industrial maintenance systems.
International Nuclear Information System (INIS)
Chen, J.-D.
2007-01-01
In this paper, the robust control problem of output dynamic observer-based control for a class of uncertain neutral systems with discrete and distributed time delays is considered. Linear matrix inequality (LMI) optimization approach is used to design the new output dynamic observer-based controls. Three classes of observer-based controls are proposed and the maximal perturbed bound is given. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls. Finally, a numerical example is given to illustrate the usefulness of the proposed method
Modelling a reliability system governed by discrete phase-type distributions
International Nuclear Information System (INIS)
Ruiz-Castro, Juan Eloy; Perez-Ocon, Rafael; Fernandez-Villodre, Gemma
2008-01-01
We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab
Modelling a reliability system governed by discrete phase-type distributions
Energy Technology Data Exchange (ETDEWEB)
Ruiz-Castro, Juan Eloy [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)], E-mail: jeloy@ugr.es; Perez-Ocon, Rafael [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)], E-mail: rperezo@ugr.es; Fernandez-Villodre, Gemma [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)
2008-11-15
We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab.
Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences
Naimzada, A. K.; Pireddu, M.
2018-05-01
We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are characterized by different preference structures. The reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is initially increasing with its visibility level, but it becomes decreasing when its visibility exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts both in the agents' consumption choices and in the population shares. More precisely, we investigate the existence of equilibria and their stability, and we perform a qualitative bifurcation analysis on varying the parameter describing the group's heterogeneity degree. From a global viewpoint, we detect, among others, multistability phenomena in which the group coexistence is dynamic, either regular or irregular, and the fashion cycle occurs. The existence of complex dynamics is proven via the method of the turbulent maps, working with homoclinic orbits. Finally, we provide a social and economic interpretation of the main scenarios.
Complexified dynamical systems
International Nuclear Information System (INIS)
Bender, Carl M; Holm, Darryl D; Hook, Daniel W
2007-01-01
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)
Nonautonomous dynamical systems
Kloeden, Peter E
2011-01-01
The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
The discrete hungry Lotka Volterra system and a new algorithm for computing matrix eigenvalues
Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa
2009-01-01
The discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra (dLV) system which stands for a prey-predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix.
About several classes of bi-orthogonal polynomials and discrete integrable systems
International Nuclear Information System (INIS)
Chang, Xiang-Ke; Chen, Xiao-Min; Hu, Xing-Biao; Tam, Hon-Wah
2015-01-01
By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry Lotka–Volterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotient–quotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided. (paper)
Decentralized control of discrete-time linear time invariant systems with input saturation
Deliu, Ciprian; Deliu, C.; Malek, Babak; Roy, Sandip; Saberi, Ali; Stoorvogel, Antonie Arij
2009-01-01
We study decentralized stabilization of discrete time linear time invariant (LTI) systems subject to actuator saturation, using LTI controllers. The requirement of stabilization under both saturation constraints and decentralization impose obvious necessary conditions on the open-loop plant, namely
The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues
International Nuclear Information System (INIS)
Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa
2009-01-01
The discrete hungry Lotka–Volterra (dhLV) system is a generalization of the discrete Lotka–Volterra (dLV) system which stands for a prey–predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix
Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2008-01-01
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally
Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters
International Nuclear Information System (INIS)
Chen Yong; Li Xin
2009-01-01
The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme. (general)
Discretizing LTI Descriptor (Regular Differential Input Systems with Consistent Initial Conditions
Directory of Open Access Journals (Sweden)
Athanasios D. Karageorgos
2010-01-01
Full Text Available A technique for discretizing efficiently the solution of a Linear descriptor (regular differential input system with consistent initial conditions, and Time-Invariant coefficients (LTI is introduced and fully discussed. Additionally, an upper bound for the error ‖x¯(kT−x¯k‖ that derives from the procedure of discretization is also provided. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena.
Control of the formation of projective synchronisation in lower-dimensional discrete-time systems
International Nuclear Information System (INIS)
Chee, C.Y.; Xu Daolin
2003-01-01
Projective synchronisation was recently observed in partially linear discrete-time systems. The scaling factor that characterises the behaviour of projective synchronisation is however unpredictable. In order to manipulate the ultimate state of the synchronisation, a control algorithm based on Schur-Chon stability criteria is proposed to direct the scaling factor onto any predestined value. In the numerical experiment, we illustrate the application on two chaotic discrete-time systems
Optimization of stochastic discrete systems and control on complex networks computational networks
Lozovanu, Dmitrii
2014-01-01
This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors' new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book's final chapter is devoted to finite horizon stochastic con...
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.
International Nuclear Information System (INIS)
Avci, E.
2007-01-01
In this paper, an automatic system is presented for word recognition using real Turkish word signals. This paper especially deals with combination of the feature extraction and classification from real Turkish word signals. A Discrete Wavelet Neural Network (DWNN) model is used, which consists of two layers: discrete wavelet layer and multi-layer perceptron. The discrete wavelet layer is used for adaptive feature extraction in the time-frequency domain and is composed of Discrete Wavelet Transform (DWT) and wavelet entropy. The multi-layer perceptron used for classification is a feed-forward neural network. The performance of the used system is evaluated by using noisy Turkish word signals. Test results showing the effectiveness of the proposed automatic system are presented in this paper. The rate of correct recognition is about 92.5% for the sample speech signals. (author)
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Directory of Open Access Journals (Sweden)
Rafał Stanisławski
2016-01-01
Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.
Directory of Open Access Journals (Sweden)
Maitraye Sen
2017-04-01
Full Text Available A discrete element model (DEM has been developed for an industrial batch bin blender in which three different types of materials are mixed. The mixing dynamics have been evaluated from a model-based study with respect to the blend critical quality attributes (CQAs which are relative standard deviation (RSD and segregation intensity. In the actual industrial setup, a sensor mounted on the blender lid is used to determine the blend composition in this region. A model-based analysis has been used to understand the mixing efficiency in the other zones inside the blender and to determine if the data obtained near the blender-lid region are able to provide a good representation of the overall blend quality. Sub-optimal mixing zones have been identified and other potential sampling locations have been investigated in order to obtain a good approximation of the blend variability. The model has been used to study how the mixing efficiency can be improved by varying the key processing parameters, i.e., blender RPM/speed, fill level/volume and loading order. Both segregation intensity and RSD reduce at a lower fill level and higher blender RPM and are a function of the mixing time. This work demonstrates the use of a model-based approach to improve process knowledge regarding a pharmaceutical mixing process. The model can be used to acquire qualitative information about the influence of different critical process parameters and equipment geometry on the mixing dynamics.
Directory of Open Access Journals (Sweden)
Arthur Coré
2017-01-01
Full Text Available This paper deals with the characterization and the numerical modelling of the collapse of composite hollow spherical structures developed to absorb energy during high velocity impacts. The structure is composed of hollow spheres (ϕ=2–30 mm made of epoxy resin and mineral powder. First of all, quasi-static and dynamic (v=5 mm·min−1 to v=2 m·s−1 compression tests are conducted at room temperature on a single sphere to study energy dissipation mechanisms. Fracture of the material appears to be predominant. A numerical model based on the discrete element method is investigated to simulate the single sphere crushing. The stress-strain-time relationship of the material based on the Ree-Eyring law is numerically implemented. The DEM modelling takes naturally into account the dynamic fracture and the crack path computed is close to the one observed experimentally in uniaxial compression. Eventually, high velocity impacts (v>100 m·s−1 of a hollow sphere on a rigid surface are conducted with an air cannon. The numerical results are in good agreement with the experimental data and demonstrate the ability of the present model to correctly describe the mechanical behavior of brittle materials at high strain rate.
The inverse problem of the calculus of variations for discrete systems
Barbero-Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián; Martín de Diego, David
2018-05-01
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.
Statistical characterization of discrete conservative systems: The web map
Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino
2017-10-01
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.
International Nuclear Information System (INIS)
Liu Wenyan; Tang, Z.P.; Liu Yunxin
2000-01-01
In recent years, more attention has been paid to a better understanding of the failure behavior and mechanism of heterogeneous materials at the meso-scale level. In this paper, the crack initiation and development in epoxy composites reinforced with short steel fibers under dynamic loading were simulated and analyzed with the 2D Discrete Meso-Element Dynamic Method. Results show that the damage process depends greatly on the binding property between matrix and fibers
Emergence in Dynamical Systems
Directory of Open Access Journals (Sweden)
John Collier
2013-12-01
Full Text Available Emergence is a term used in many contexts in current science; it has become fashionable. It has a traditional usage in philosophy that started in 1875 and was expanded by J. S. Mill (earlier, under a different term and C. D. Broad. It is this form of emergence that I am concerned with here. I distinguish it from uses like ‘computational emergence,’ which can be reduced to combinations of program steps, or its application to merely surprising new features that appear in complex combinations of parts. I will be concerned specifically with ontological emergence that has the logical properties required by Mill and Broad (though there might be some quibbling about the details of their views. I restrict myself to dynamical systems that are embodied in processes. Everything that we can interact with through sensation or action is either dynamical or can be understood in dynamical terms, so this covers all comprehensible forms of emergence in the strong (nonreducible sense I use. I will give general dynamical conditions that underlie the logical conditions traditionally assigned to emergence in nature.The advantage of this is that, though we cannot test logical conditions directly, we can test dynamical conditions. This gives us an empirical and realistic form of emergence, contrary those who say it is a matter of perspective.
What are System Dynamics Insights?
Stave, K.; Zimmermann, N. S.; Kim, H.
2016-01-01
This paper explores the concept of system dynamics insights. In our field, the term “insight” is generally understood to mean dynamic insight, that is, a deep understanding about the relationship between structure and behavior. We argue this is only one aspect of the range of insights possible from system dynamics activities, and describe a broader range of potential system dynamics insights. We also propose an initial framework for discussion that relates different types of system dynamics a...
The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems
P.J. Collins (Pieter); A. Goldsztejn
2008-01-01
htmlabstractThis paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems. The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs. In
Counting and classifying attractors in high dimensional dynamical systems.
Bagley, R J; Glass, L
1996-12-07
Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
International Nuclear Information System (INIS)
Zhang Yu-Feng; Tam, Honwah
2016-01-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A_1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A_1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. (paper)
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
DEFF Research Database (Denmark)
Mohd. Azam, Sazuan Nazrah
2017-01-01
In this paper, we used the modified quadruple tank system that represents a multi-input-multi-output (MIMO) system as an example to present the realization of a linear discrete-time state space model and to obtain the state estimation using Kalman filter in a methodical mannered. First, an existing...... part of the Kalman filter is used to estimates the current state, based on the model and the measurements. The static and dynamic Kalman filter is compared and all results is demonstrated through simulations....
Perfect discretization of path integrals
Steinhaus, Sebastian
2011-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...
Adaptive discrete rate and power transmission for spectrum sharing systems
Abdallah, Mohamed M.
2012-04-01
In this paper we develop a framework for optimizing the performance of the secondary link in terms of the average spectral efficiency assuming quantized channel state information (CSI) of the secondary and the secondary-to-primary interference channels available at the secondary transmitter. We consider the problem under the constraints of maximum average interference power levels at the primary receiver. We develop a sub-optimal computationally efficient iterative algorithm for finding the optimal CSI quantizers as well as the discrete power and rate employed at the cognitive transmitter for each quantized CSI level so as to maximize the average spectral efficiency. We show via analysis and simulations that the proposed algorithm converges for Rayleigh fading channels. Our numerical results give the number of bits required to sufficiently represent the CSI to achieve almost the maximum average spectral efficiency attained using full knowledge of the CSI. © 2012 IEEE.
Discrete Event System Based Pyroprocessing Modeling and Simulation: Oxide Reduction
International Nuclear Information System (INIS)
Lee, H. J.; Ko, W. I.; Choi, S. Y.; Kim, S. K.; Hur, J. M.; Choi, E. Y.; Im, H. S.; Park, K. I.; Kim, I. T.
2014-01-01
Dynamic changes according to the batch operation cannot be predicted in an equilibrium material flow. This study began to build a dynamic material balance model based on the previously developed pyroprocessing flowsheet. As a mid- and long-term research, an integrated pyroprocessing simulator is being developed at the Korea Atomic Energy Research Institute (KAERI) to cope with a review on the technical feasibility, safeguards assessment, conceptual design of facility, and economic feasibility evaluation. The most fundamental thing in such a simulator development is to establish the dynamic material flow framework. This study focused on the operation modeling of pyroprocessing to implement a dynamic material flow. As a case study, oxide reduction was investigated in terms of a dynamic material flow. DES based modeling was applied to build a pyroprocessing operation model. A dynamic material flow as the basic framework for an integrated pyroprocessing was successfully implemented through ExtendSim's internal database and item blocks. Complex operation logic behavior was verified, for example, an oxide reduction process in terms of dynamic material flow. Compared to the equilibrium material flow, a model-based dynamic material flow provides such detailed information that a careful analysis of every batch is necessary to confirm the dynamic material balance results. With the default scenario of oxide reduction, the batch mass balance was verified in comparison with a one-year equilibrium mass balance. This study is still under progress with a mid-and long-term goal, the development of a multi-purpose pyroprocessing simulator that is able to cope with safeguards assessment, economic feasibility, technical evaluation, conceptual design, and support of licensing for a future pyroprocessing facility
Directory of Open Access Journals (Sweden)
Fernando Gómez-Salas
2015-01-01
Full Text Available This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.
Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure
Diethert, A.; Finster, F.; Schiefeneder, D.
As toy models for space-time at the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the particles as described by a variational principle both analytically and numerically. We find an effect of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure.
Control of Discrete-Event Systems Automata and Petri Net Perspectives
Silva, Manuel; Schuppen, Jan
2013-01-01
Control of Discrete-event Systems provides a survey of the most important topics in the discrete-event systems theory with particular focus on finite-state automata, Petri nets and max-plus algebra. Coverage ranges from introductory material on the basic notions and definitions of discrete-event systems to more recent results. Special attention is given to results on supervisory control, state estimation and fault diagnosis of both centralized and distributed/decentralized systems developed in the framework of the Distributed Supervisory Control of Large Plants (DISC) project. Later parts of the text are devoted to the study of congested systems though fluidization, an over approximation allowing a much more efficient study of observation and control problems of timed Petri nets. Finally, the max-plus algebraic approach to the analysis and control of choice-free systems is also considered. Control of Discrete-event Systems provides an introduction to discrete-event systems for readers that are not familiar wi...
Wisdom, Jack
2002-01-01
In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.
Controlling chaos in dynamical systems described by maps
International Nuclear Information System (INIS)
Crispin, Y.; Marduel, C.
1994-01-01
The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps
Directory of Open Access Journals (Sweden)
Wai Kuan Yip
2007-01-01
Full Text Available We introduce a novel method for secure computation of biometric hash on dynamic hand signatures using BioPhasor mixing and discretization. The use of BioPhasor as the mixing process provides a one-way transformation that precludes exact recovery of the biometric vector from compromised hashes and stolen tokens. In addition, our user-specific discretization acts both as an error correction step as well as a real-to-binary space converter. We also propose a new method of extracting compressed representation of dynamic hand signatures using discrete wavelet transform (DWT and discrete fourier transform (DFT. Without the conventional use of dynamic time warping, the proposed method avoids storage of user's hand signature template. This is an important consideration for protecting the privacy of the biometric owner. Our results show that the proposed method could produce stable and distinguishable bit strings with equal error rates (EERs of and for random and skilled forgeries for stolen token (worst case scenario, and for both forgeries in the genuine token (optimal scenario.
Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L
2013-12-01
In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.
Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
Rovny, Jared; Blum, Robert L.; Barrett, Sean E.
2018-05-01
A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.
Perfect discretization of path integrals
International Nuclear Information System (INIS)
Steinhaus, Sebastian
2012-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Perfect discretization of path integrals
Steinhaus, Sebastian
2012-05-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Chang, Insu
The objective of the thesis is to introduce a relatively general nonlinear controller/estimator synthesis framework using a special type of the state-dependent Riccati equation technique. The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided. Stability of the D-SDRE feedback system is established using Lyapunov stability approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller. Stability condition of the CD-SDRE controller is analyzed by using a switched system. The use of CD-SDRE scheme in the presence of constraints is then systematically demonstrated by applying this scheme to problems of spacecraft formation orbit reconfiguration under limited performance on thrusters. Simulation results demonstrate the efficacy and reliability of the proposed CD-SDRE. The CD-SDRE technique is further investigated in a case where there are uncertainties in nonlinear systems to be controlled. First, the system stability under each of the controllers in the robust CD-SDRE technique is separately established. The stability of the closed-loop system under the robust CD-SDRE controller is then proven based on the stability of each control system comprising switching configuration. A high fidelity dynamical model of spacecraft attitude motion in 3-dimensional space is derived with a partially filled fuel tank, assumed to have the first fuel slosh mode. The proposed robust CD-SDRE controller is then applied to the spacecraft attitude control system to stabilize its motion in the presence of uncertainties characterized by the first fuel slosh mode. The performance of the robust CD-SDRE technique is discussed. Subsequently
Flow Dynamics of green sand in the DISAMATIC moulding process using Discrete element method (DEM)
International Nuclear Information System (INIS)
Hovad, E; Walther, J H; Thorborg, J; Hattel, J H; Larsen, P
2015-01-01
The DISAMATIC casting process production of sand moulds is simulated with DEM (discrete element method). The main purpose is to simulate the dynamics of the flow of green sand, during the production of the sand mould with DEM. The sand shot is simulated, which is the first stage of the DISAMATIC casting process. Depending on the actual casting geometry the mould can be geometrically quite complex involving e.g. shadowing effects and this is directly reflected in the sand flow during the moulding process. In the present work a mould chamber with “ribs” at the walls is chosen as a baseline geometry to emulate some of these important conditions found in the real moulding process. The sand flow is simulated with the DEM and compared with corresponding video footages from the interior of the chamber during the moulding process. The effect of the rolling resistance and the static friction coefficient is analysed and discussed in relation to the experimental findings. (paper)
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2018-06-01
In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.
A discrete particle model reproducing collective dynamics of a bee swarm.
Bernardi, Sara; Colombi, Annachiara; Scianna, Marco
2018-02-01
In this article, we present a microscopic discrete mathematical model describing collective dynamics of a bee swarm. More specifically, each bee is set to move according to individual strategies and social interactions, the former involving the desire to reach a target destination, the latter accounting for repulsive/attractive stimuli and for alignment processes. The insects tend in fact to remain sufficiently close to the rest of the population, while avoiding collisions, and they are able to track and synchronize their movement to the flight of a given set of neighbors within their visual field. The resulting collective behavior of the bee cloud therefore emerges from non-local short/long-range interactions. Differently from similar approaches present in the literature, we here test different alignment mechanisms (i.e., based either on an Euclidean or on a topological neighborhood metric), which have an impact also on the other social components characterizing insect behavior. A series of numerical realizations then shows the phenomenology of the swarm (in terms of pattern configuration, collective productive movement, and flight synchronization) in different regions of the space of free model parameters (i.e., strength of attractive/repulsive forces, extension of the interaction regions). In this respect, constraints in the possible variations of such coefficients are here given both by reasonable empirical observations and by analytical results on some stability characteristics of the defined pairwise interaction kernels, which have to assure a realistic crystalline configuration of the swarm. An analysis of the effect of unconscious random fluctuations of bee dynamics is also provided. Copyright © 2018 Elsevier Ltd. All rights reserved.
Robust Moving Horizon H∞ Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays
Directory of Open Access Journals (Sweden)
F. Yıldız Tascikaraoglu
2014-01-01
Full Text Available In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.
Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling.
Fačkovec, B; Vanden-Eijnden, E; Wales, D J
2015-07-28
A method is derived to coarse-grain the dynamics of complex molecular systems to a Markov jump process (MJP) describing how the system jumps between cells that fully partition its state space. The main inputs are relaxation times for each pair of cells, which are shown to be robust with respect to positioning of the cell boundaries. These relaxation times can be calculated via molecular dynamics simulations performed in each cell separately and are used in an efficient estimator for the rate matrix of the MJP. The method is illustrated through applications to Sinai billiards and a cluster of Lennard-Jones discs.
The Basics of Anisotropy-Based Analysis of Discrete Time-Invariant Systems
Directory of Open Access Journals (Sweden)
I. R. Belov
2017-01-01
Full Text Available When investigating a behavior of dynamical systems, we should take into account the external noises, which have an effect on the system. The article introduces a concept of the anisotropy-based norm of the system as one of the ways to describe the measure of the effect of external disturbances on the system. The definition of the anisotropic norm includes some concepts from information theory, such as relative entropy and anisotropy. The theoretical section at the beginning of the article describes these definitions. The considered norm of the system can be evaluated in several ways. The article examines two methods - in the frequency domain and in the state space. To find the norm in the state space it is necessary to find the solution of the Riccati equation. This problem is rather laborious. So the algorithms to avoid the solution of Riccati equation are used in application of anisotropy-based norm’s evaluation methods. The principle of these algorithms is replacement of Riccati equation by the system of linear matrix inequalities. The software implementation of methods under consideration is designed using the MATLAB packages. The calculation results of the anisotropy-based norm for a given linear discrete system are obtained using this program. The article presents these results as graphs.This article enters into the Master's qualifying work "Basic quality criteria in the theory of linear systems". In this paper we consider various quality criteria, the solution of the optimal control problem for each of them, and compare the results obtained for different criteria. The anisotropy-based norm considered in the article is one of the quality criteria.
On Discrete Time Control of Continuous Time Systems
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
This report is meant as a supplement or an extension to the material used in connection to or after the courses Stochastic Adaptive Control (02421) and Static and Dynamic Optimization (02711) given at the department Department of Informatics and Mathematical Modelling, The Technical University...
Dynamical Signatures of Living Systems
Zak, M.
1999-01-01
One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion
Dynamical systems with applications using MATLAB
Lynch, Stephen
2014-01-01
This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox™, and the Symbolic Math Toolbox™, including MuPAD. Features new to the second edition include, sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; chapters on image processing and binary oscillator computing; hundreds of new illustrations, examples, and exercises with solutions; and over eighty up-to-date MATLAB® program files and Simulink model files available online. These files were voted MATLAB® Central Pick of the Week in July 2013. The hands-on approach of Dynamical Systems with Applications using MATLAB®, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equ...
Adaptive control of discrete-time chaotic systems: a fuzzy control approach
International Nuclear Information System (INIS)
Feng Gang; Chen Guanrong
2005-01-01
This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T-S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm
International Nuclear Information System (INIS)
Tsuchida, Takayuki
2010-01-01
We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.
Carlos Varas, Álvaro E; Peters, E A J F; Kuipers, J A M
2017-05-17
We report a computational fluid dynamics-discrete element method (CFD-DEM) simulation study on the interplay between mass transfer and a heterogeneous catalyzed chemical reaction in cocurrent gas-particle flows as encountered in risers. Slip velocity, axial gas dispersion, gas bypassing, and particle mixing phenomena have been evaluated under riser flow conditions to study the complex system behavior in detail. The most important factors are found to be directly related to particle cluster formation. Low air-to-solids flux ratios lead to more heterogeneous systems, where the cluster formation is more pronounced and mass transfer more influenced. Falling clusters can be partially circumvented by the gas phase, which therefore does not fully interact with the cluster particles, leading to poor gas-solid contact efficiencies. Cluster gas-solid contact efficiencies are quantified at several gas superficial velocities, reaction rates, and dilution factors in order to gain more insight regarding the influence of clustering phenomena on the performance of riser reactors.
Cosmological dynamical systems
Leon, Genly
2011-01-01
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincar\\'e compactification process allowing to construct a global phase space containing all the cosmological information in both finite and infinite...
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 ...
Discrete-time Calogero-Moser system and Lagrangian 1-form structure
International Nuclear Information System (INIS)
Yoo-Kong, Sikarin; Lobb, Sarah; Nijhoff, Frank
2011-01-01
We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time and continuous time, as a first example of a Lagrangian 1-form structure in the sense of the recent paper (Lobb and Nijhoff 2009 J. Phys. A: Math. Theor.42 454013). The discrete-time model of the CM system was established some time ago arising as a pole reduction of a semi-discrete version of the Kadomtsev-Petviashvili (KP) equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper, we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation and the level of the CM system, we establish the proper Lagrangian 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in Lobb and Nijhoff (2009), for the simpler case of Lagrangian 1-forms. (paper)
Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun
2018-07-01
Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.
Bounded Model Checking and Inductive Verification of Hybrid Discrete-Continuous Systems
DEFF Research Database (Denmark)
Becker, Bernd; Behle, Markus; Eisenbrand, Fritz
2004-01-01
We present a concept to signicantly advance the state of the art for bounded model checking (BMC) and inductive verication (IV) of hybrid discrete-continuous systems. Our approach combines the expertise of partners coming from dierent domains, like hybrid systems modeling and digital circuit veri...
Nonparametric Estimation of Interval Reliability for Discrete-Time Semi-Markov Systems
DEFF Research Database (Denmark)
Georgiadis, Stylianos; Limnios, Nikolaos
2016-01-01
In this article, we consider a repairable discrete-time semi-Markov system with finite state space. The measure of the interval reliability is given as the probability of the system being operational over a given finite-length time interval. A nonparametric estimator is proposed for the interval...
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.
Less Conservative ℋ∞ Fuzzy Control for Discrete-Time Takagi-Sugeno Systems
Directory of Open Access Journals (Sweden)
Leonardo Amaral Mozelli
2011-01-01
Full Text Available New analysis and control design conditions of discrete-time fuzzy systems are proposed. Using fuzzy Lyapunov's functions and introducing slack variables, less conservative conditions are obtained. The controller guarantees system stabilization and ℋ∞ performance. Numerical tests and a practical experiment in Chua's circuit are presented to show the effectiveness.
Communication scheduling in robust self-triggered MPC for linear discrete-time systems
Brunner, F.D.; Gommans, T.M.P.; Heemels, W.P.M.H.; Allgöwer, F.
2015-01-01
We consider a networked control system consisting of a physical plant, an actuator, a sensor, and a controller that is connected to the actuator and sensor via a communication network. The plant is described by a linear discrete-time system subject to additive disturbances. In order to reduce the
A NEW STRATEGY FOR IMPROVING FEATURE SETS IN A DISCRETE HMMBASED HANDWRITING RECOGNITION SYSTEM
Grandidier, F.; Sabourin, R.; Suen, C.Y.; Gilloux, M.
2004-01-01
In this paper we introduce a new strategy for improving a discrete HMMbased handwriting recognition system, by integrating several information sources from specialized feature sets. For a given system, the basic idea is to keep the most discriminative features, and to replace the others with new
Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.
Brocklehurst, Paul; Ni, Haibo; Zhang, Henggui; Ye, Jianqiao
2017-01-01
We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano
Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.
Directory of Open Access Journals (Sweden)
Paul Brocklehurst
Full Text Available We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM. Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of
Kabalyants, Petr; Nosov, Konstantin; Bespalov, Yuri
2017-01-01
The paper aims at building the model of relations of biodiversity and stability at different levels of organization of living matter with the use of discrete dynamical models. The relations revealed in the study are illustrated by case studies of zooplankton community of the eutrophicated lake and the colorimetric parameters of the microalgae community of phytobenthos and phytoperiphyton. The results offer: (1) new approaches to estimating the risk of mass development of toxic cyanobacteria i...
Out-of-order parallel discrete event simulation for electronic system-level design
Chen, Weiwei
2014-01-01
This book offers readers a set of new approaches and tools a set of tools and techniques for facing challenges in parallelization with design of embedded systems.? It provides an advanced parallel simulation infrastructure for efficient and effective system-level model validation and development so as to build better products in less time.? Since parallel discrete event simulation (PDES) has the potential to exploit the underlying parallel computational capability in today's multi-core simulation hosts, the author begins by reviewing the parallelization of discrete event simulation, identifyin
Discrete Displacement Hydraulic Power Take-Off System for the Wavestar Wave Energy Converter
DEFF Research Database (Denmark)
Hansen, Rico Hjerm; Kramer, Morten; Vidal, Enrique
2013-01-01
. This is achieved by using special multi-chambered cylinders, where the different chambers may be connected to the available system pressures using fast on/off valves. Resultantly, a Discrete Displacement Cylinder (DDC) is created, allowing near loss free discrete force control. This paper presents a complete PTO...... system for a 20 float Wavestar based on the DDC. The WEC and PTO is rigorously modeled from incident waves to the electric output to the grid. The resulting model of +600 states is simulated in different irregular seas, showing that power conversion efficiencies above 70% from input power to electrical...
Elucidation of amyloid beta-protein oligomerization mechanisms: discrete molecular dynamics study.
Urbanc, B; Betnel, M; Cruz, L; Bitan, G; Teplow, D B
2010-03-31
Oligomers of amyloid beta-protein (Abeta) play a central role in the pathology of Alzheimer's disease. Of the two predominant Abeta alloforms, Abeta(1-40) and Abeta(1-42), Abeta(1-42) is more strongly implicated in the disease. We elucidated the structural characteristics of oligomers of Abeta(1-40) and Abeta(1-42) and their Arctic mutants, [E22G]Abeta(1-40) and [E22G]Abeta(1-42). We simulated oligomer formation using discrete molecular dynamics (DMD) with a four-bead protein model, backbone hydrogen bonding, and residue-specific interactions due to effective hydropathy and charge. For all four peptides under study, we derived the characteristic oligomer size distributions that were in agreement with prior experimental findings. Unlike Abeta(1-40), Abeta(1-42) had a high propensity to form paranuclei (pentameric or hexameric) structures that could self-associate into higher-order oligomers. Neither of the Arctic mutants formed higher-order oligomers, but [E22G]Abeta(1-40) formed paranuclei with a similar propensity to that of Abeta(1-42). Whereas the best agreement with the experimental data was obtained when the charged residues were modeled as solely hydrophilic, further assembly from spherical oligomers into elongated protofibrils was induced by nonzero electrostatic interactions among the charged residues. Structural analysis revealed that the C-terminal region played a dominant role in Abeta(1-42) oligomer formation whereas Abeta(1-40) oligomerization was primarily driven by intermolecular interactions among the central hydrophobic regions. The N-terminal region A2-F4 played a prominent role in Abeta(1-40) oligomerization but did not contribute to the oligomerization of Abeta(1-42) or the Arctic mutants. The oligomer structure of both Arctic peptides resembled Abeta(1-42) more than Abeta(1-40), consistent with their potentially more toxic nature.
Directory of Open Access Journals (Sweden)
Mengjuan Cao
2014-01-01
Full Text Available The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.
International Nuclear Information System (INIS)
Rousseau, J.
2009-07-01
That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)
Discrete-time sliding mode control for MR vehicle suspension system
Energy Technology Data Exchange (ETDEWEB)
Sohn, J W; Choi, S B [Smart Structures and Systems Laboratory, Department of Mechanical Engineering, Inha University, Incheon 402-751 (Korea, Republic of); Wereley, N M [Smart Structures Laboratory, Department of Aerospace Engineering, University of Maryland, College Park, MD 20742 (United States)], E-mail: seungbok@inha.ac.kr
2009-02-01
This paper presents control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers via a discrete-time sliding mode control algorithm (DSMC). A cylindrical MR damper is designed by incorporating Bingham model of the MR fluid and the field-dependent damping characteristics of the MR damper are evaluated. A full-vehicle suspension model installed with independent four MR dampers is constructed and the governing equations which include vertical, pitch and roll motion are derived. A discrete-time control model is established with considering system uncertainties and a discrete-time sliding mode controller which has inherent robustness to model uncertainty and external disturbance is formulated. Vibration control performances under bump excitation are evaluated and presented.
Discrete-time sliding mode control for MR vehicle suspension system
International Nuclear Information System (INIS)
Sohn, J W; Choi, S B; Wereley, N M
2009-01-01
This paper presents control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers via a discrete-time sliding mode control algorithm (DSMC). A cylindrical MR damper is designed by incorporating Bingham model of the MR fluid and the field-dependent damping characteristics of the MR damper are evaluated. A full-vehicle suspension model installed with independent four MR dampers is constructed and the governing equations which include vertical, pitch and roll motion are derived. A discrete-time control model is established with considering system uncertainties and a discrete-time sliding mode controller which has inherent robustness to model uncertainty and external disturbance is formulated. Vibration control performances under bump excitation are evaluated and presented.
Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach
Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer
2018-02-01
This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.
Application of the Sumudu Transform to Discrete Dynamic Systems
Asiru, Muniru Aderemi
2003-01-01
The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…
Design of an optimal preview controller for linear discrete-time descriptor systems with state delay
Cao, Mengjuan; Liao, Fucheng
2015-04-01
In this paper, the linear discrete-time descriptor system with state delay is studied, and a design method for an optimal preview controller is proposed. First, by using the discrete lifting technique, the original system is transformed into a general descriptor system without state delay in form. Then, taking advantage of the first-order forward difference operator, we construct a descriptor augmented error system, including the state vectors of the lifted system, error vectors, and desired target signals. Rigorous mathematical proofs are given for the regularity, stabilisability, causal controllability, and causal observability of the descriptor augmented error system. Based on these, the optimal preview controller with preview feedforward compensation for the original system is obtained by using the standard optimal regulator theory of the descriptor system. The effectiveness of the proposed method is shown by numerical simulation.
Dynamical systems with applications using Mathematica
Lynch, Stephen
2017-01-01
This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite. Taking a hands-on approach, the reader is guided from basic concepts to modern research topics. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. The book begins with an efficient tutorial introduction to Mathematica, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at: http://library.wolfram.com/infocenter/Books/9563/ The author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum, though references are included for the inquisitive reader. The book is intended for senior undergraduate and graduate students as well as w...
Dynamics of Multibody Systems Near Lagrangian Points
Wong, Brian
This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term
the evaluation of a discrete automatic analysis system
African Journals Online (AJOL)
1971-05-29
May 29, 1971 ... analytical systems have appeared on the market (for a general review, see ... The testing and evaluation of new scientific equipment has in recent years .... automation into the clinical chemistry laboratory, it is necessary to ...
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
Synthesis of adaptive traffic control discrete neminimalno-phase system
Directory of Open Access Journals (Sweden)
В.М. Азарсков
2007-01-01
Full Text Available An adaptive approach to synthesizing the digital tracking system with direct set-point coupling is extended under conditions when a plant is non-minimum phase. Some bounded set of belonging of servo drive unknown parameters vector is believed to be known. The object’s model non-singularity condition is established. The asymptotical properties of control system are studied. Simulation results are given.
Synchronization dynamics of two different dynamical systems
International Nuclear Information System (INIS)
Luo, Albert C.J.; Min Fuhong
2011-01-01
Highlights: → Synchronization dynamics of two distinct dynamical systems. → Synchronization, de-synchronization and instantaneous synchronization. → A controlled pendulum synchronizing with the Duffing oscillator. → Synchronization invariant set. → Synchronization parameter map. - Abstract: In this paper, synchronization dynamics of two different dynamical systems is investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for the synchronization, de-synchronization and instantaneous synchronization (penetration or grazing) are presented. Using such a synchronization theory, the synchronization of a controlled pendulum with the Duffing oscillator is systematically discussed as a sampled problem, and the corresponding analytical conditions for the synchronization are presented. The synchronization parameter study is carried out for a better understanding of synchronization characteristics of the controlled pendulum and the Duffing oscillator. Finally, the partial and full synchronizations of the controlled pendulum with periodic and chaotic motions are presented to illustrate the analytical conditions. The synchronization of the Duffing oscillator and pendulum are investigated in order to show the usefulness and efficiency of the methodology in this paper. The synchronization invariant domain is obtained. The technique presented in this paper should have a wide spectrum of applications in engineering. For example, this technique can be applied to the maneuvering target tracking, and the others.
Heterogeneous System Architectures from APUs to discrete GPUs
CERN. Geneva
2013-01-01
We will present the Heterogeneous Systems Architectures that new AMD processors are bringing with the new GCN based GPUs and the new APUs. We will show how together they represent a huge step forward for programming flexibility and performance efficiently for Compute.
Systems approaches to study root architecture dynamics
Directory of Open Access Journals (Sweden)
Candela eCuesta
2013-12-01
Full Text Available The plant root system is essential for providing anchorage to the soil, supplying minerals and water, and synthesizing metabolites. It is a dynamic organ modulated by external cues such as environmental signals, water and nutrients availability, salinity and others. Lateral roots are initiated from the primary root post-embryonically, after which they progress through discrete developmental stages which can be independently controlled, providing a high level of plasticity during root system formation.Within this review, main contributions are presented, from the classical forward genetic screens to the more recent high-throughput approaches, combined with computer model predictions, dissecting how lateral roots and thereby root system architecture is established and developed.
On constructing optimistic simulation algorithms for the discrete event system specification
International Nuclear Information System (INIS)
Nutaro, James J.
2008-01-01
This article describes a Time Warp simulation algorithm for discrete event models that are described in terms of the Discrete Event System Specification (DEVS). The article shows how the total state transition and total output function of a DEVS atomic model can be transformed into an event processing procedure for a logical process. A specific Time Warp algorithm is constructed around this logical process, and it is shown that the algorithm correctly simulates a DEVS coupled model that consists entirely of interacting atomic models. The simulation algorithm is presented abstractly; it is intended to provide a basis for implementing efficient and scalable parallel algorithms that correctly simulate DEVS models
International Nuclear Information System (INIS)
Choi, Jong Gyun; Seong, Poong Hyun
2001-01-01
This article describes a combinatorial model for estimating the reliability of the embedded digital system by means of discrete function theory and software control flow. This model includes a coverage model for fault processing mechanisms implemented in digital system. Furthermore, the model considers the interaction between hardware and software. The fault processing mechanisms make it difficult for many types of components in digital system to be treated as binary state, good or bad. The discrete function theory provides a complete analysis of multi-state system as which the digital system can be regarded Through adaptation software control flow to discrete function theory, the HW/SW interaction is considered for estimation of the reliability of digital system. Using this model, we predict the reliability of one board controller in a digital system, Interposing Logic System(ILS), which is installed in YGN nuclear power units 3 and 4. Since the proposed model is general combinatinal model, the simplification of this model becomes a conservative model that treats the system as binary state. Moreover, if information for coverage factor of fault tolerance mechanisms implemented in system through fault injection experiment is obtained, this model can consider detailed interaction of system components
Passive Fault-tolerant Control of Discrete-time Piecewise Affine Systems against Actuator Faults
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Izadi-Zamanabadi, Roozbeh; Bak, Thomas
2012-01-01
In this paper, we propose a new method for passive fault-tolerant control of discrete time piecewise affine systems. Actuator faults are considered. A reliable piecewise linear quadratic regulator (LQR) state feedback is designed such that it can tolerate actuator faults. A sufficient condition f...... is illustrated on a numerical example and a two degree of freedom helicopter....
Property - preserving convergent sequences of invariant sets for linear discrete - time systems
Athanasopoulos, N.; Lazar, M.; Bitsoris, G.
2014-01-01
Abstract: New sequences of monotonically increasing sets are introduced, for linear discrete-time systems subject to input and state constraints. The elements of the set sequences are controlled invariant and admissible regions of stabilizability. They are generated from the iterative application of
Directory of Open Access Journals (Sweden)
Xinggui Liu
2011-01-01
Full Text Available In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.
International Nuclear Information System (INIS)
Chen, S.-F.
2009-01-01
The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then, the es...
DEFF Research Database (Denmark)
Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus
1998-01-01
A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp...
Multiple periodic solutions for a fourth-order discrete Hamiltonian system
Directory of Open Access Journals (Sweden)
Yongkun Li
2010-12-01
Full Text Available By means of a three critical points theorem proposed by Brezis and Nirenberg and a general version of Mountain Pass Theorem, we obtain some multiplicity results for periodic solutions of a fourth-order discrete Hamiltonian system Δ4u(t-2+∇ F(t,u(t=0 for all t∈ Z.
Controllability of a Class of Bimodal Discrete-Time Piecewise Linear Systems
Yurtseven, E.; Camlibel, M.K.; Heemels, W.P.M.H.
2013-01-01
In this paper we will provide algebraic necessary and sufficient conditions for the controllability/reachability/null controllability of a class of bimodal discrete-time piecewise linear systems including several instances of interest that are not covered by existing works which focus primarily on
Bovens, M.A.P.; Zouridis, S.
2002-01-01
The use of ICT is rapidly changing the structure of a number of large executive public agencies. They used to be machine bureaucracies in which street level officials exercised ample administrative discretion in dealing with individual clients. This was kept in check by elaborate systems of external
Decentralized control of discrete-time linear time invariant systems with input saturation
Deliu, C.; Deliu, Ciprian; Malek, Babak; Roy, Sandip; Saberi, Ali; Stoorvogel, Antonie Arij
We study decentralized stabilization of discrete-time linear time invariant (LTI) systems subject to actuator saturation, using LTI controllers. The requirement of stabilization under both saturation constraints and decentralization impose obvious necessary conditions on the open-loop plant, namely
Direct Adaptive Control of a Class of Nonlinear Discrete-Time Systems
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon
2004-01-01
In this paper we deal with direct adaptive control of a specific class of discrete-time SISO systems, where the nonlinearities are convex and an upper bound is known. We use a control law based on a linear combination of a set of globally uniformly bounded basis functions with compact support, wh...
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Discrete Address Beacon System (DABS) Baseline Test and Evaluation.
1980-04-01
maturing of the DABS/Automatic Traffic Advisory and Resolution Service ( ATARS ) system concept, would require further study and test prior to issuance of...surveillance, Automatic Traffic Advisory and Resolution Service ( ATARS ) and communications capabilities required for air traffic control (ATC) in the...1980’s and 1990’s. Compatibility with ATCRBS has been emphasized to permit an extended and economical transition. The requirement for the development
Discrete changes of current statistics in periodically driven stochastic systems
International Nuclear Information System (INIS)
Chernyak, Vladimir Y; Sinitsyn, N A
2010-01-01
We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in the evolution of the moment generating function which is akin to the topological geometric phase in the evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd numbers of particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to this sign change should enclose specific degeneracy points in the space of control parameters. The relation between the topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel–Whitney class of topological invariants. (letter)
Reducing Fatigue Loading Due to Pressure Shift in Discrete Fluid Power Force Systems
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik Clemmensen
2016-01-01
power force system. The current paper investigates the correlation between pressure oscillations in the cylinder chambers and valve flow in the manifold. Furthermore, the correlation between the pressure shifting time and the pressure overshoot is investigated. The study therefore focus on how to shape......Discrete Fluid Power Force Systems is one of the topologies gaining focus in the pursuit of lowering energy losses in fluid power transmission systems. The cylinder based Fluid Power Force System considered in this article is constructed with a multi-chamber cylinder, a number of constant pressure...... oscillations in the cylinder chamber, especially for systems with long connections between the cylinder and the valve manifold. Hose pressure oscillations will induce oscillations in the produced piston force. Hence, pressure oscillations may increase the fatigue loading on systems employing a discrete fluid...
Directory of Open Access Journals (Sweden)
M. De la Sen
2018-05-01
Full Text Available This paper presents and discusses the stability of a discrete multirate sampling system whose sets of sampling rates (or sampling periods are the integer multiple of those operating on all the preceding substates. Each of such substates is associated with a particular sampling rate. The sufficiency-type stability conditions are derived based on simple conditions on the norm, spectral radius and numerical radius of the matrix of the dynamics of a system parameterized at the largest sampling period.
A new extended H∞ filter for discrete nonlinear systems
Institute of Scientific and Technical Information of China (English)
张永安; 周荻; 段广仁
2004-01-01
Nonlinear estimation problem is investigated in this paper. By extension of a linear H∞ estimation with corrector-predictor form to nonlinear cases, a new extended H∞ filter is proposed for time-varying discretetime nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H∞ bound performs better than the EKF.
Energy Optimal Tracking Control with Discrete Fluid Power Systems using Model Predictive Control
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Asmussen, Magnus Færing; Bech, Michael Møller
2017-01-01
For Discrete Displacement Cylinder (DDC) drives the control task lies in choosing force level. Hence, which force level to apply and thereby which pressure level each cylinder chambers shall be connected to. The DDC system is inherently a force system why often a force reference is generated...... and compared to a PID like tracking controller combined with a FSA. The results indicate that the energy efficiency of position tracking DDC systems may be improved significantly by using the MPC algorithm....
Non-commutative Chern numbers for generic aperiodic discrete systems
Bourne, Chris; Prodan, Emil
2018-06-01
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a unifying theoretical framework for topological electronic, photonic, phononic etc (aperiodic) systems. We then discuss, in physical terms, the philosophy behind an operator theoretic analysis used to systematize such systems. A model calculation of the Hall conductance of a 2-dimensional amorphous lattice is given, where we present numerical evidence of its quantization in the mobility gap regime. Motivated by such facts, we then present the main result of our work, which is the extension of the Chern number formulas to Hamiltonians associated to lattices without a canonical labeling of the sites, together with index theorems that assure the quantization and stability of these Chern numbers in the mobility gap regime. Our results cover a broad range of applications, in particular, those involving quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically generated) lattices.