Discrete Stochastic Dynamical Systems Research Articles

Adaptive Algorithm of Maneuvering Target Tracking in Complex Jamming Situation for Multifunctional Radar with Phased Antenna Array

Adaptive multimodel algorithms based on the target movement model in the form of discrete stochastic dynamic system with random structure are adequate to the problem of target tracking based on data of the multifunctional radar station (MFRS) with phased antenna array (PAA) under conditions of complex dynamically varying signal and jamming situation. This study presents an optimal and quasioptimal algorithms of adaptive estimation of movement parameters of maneuvering targets in the Cartesian coordinate system for MFRS with PAA based on the mathematical tools of mixed Markov processes in discrete time. They describe the evolution of joint a posteriori probability density of the vector of target movement parameters and switching variable determining the mode of its movement, while the filters implementing them are referred to the class of devices with feedbacks between channels. The identification of blips in the tracking strobe is performed in the spherical coordinate system by selecting the blip, which is the closest to the strobe center. The efficiency analysis of the developed tracking algorithm is performed by using the test paths of two targets with different intensities of the maneuver and parameters of tracking modes. The accuracy characteristics of adaptive filter and indicators of the tracking efficiency at different false alarm probabilities have been determined.

Mean-Potential Law in Evolutionary Games

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1/3 law of evolutionary games, introduced by Nowak etal. [Nature, 2004], follows from a more general mean-potential law.

Discrete event simulation of crop operations in sweet pepper in support of work method innovation

Greenhouse Work Simulation, GWorkS, is a model that simulates crop operations in greenhouses for the purpose of analysing work methods. GWorkS is a discrete event model that approaches reality as a discrete stochastic dynamic system. GWorkS was developed and validated using cut-rose as a case crop for which two cultivation systems exist, the path-based system and the mobile cultivation system. The focus of this paper is horizontal extension of GWorkS to sweet pepper, which is characterised by high crop-related labour effort and costs. For sweet pepper, international research aiming at automation of sweet pepper harvest is ongoing. Dynamic process simulation and analysis may contribute strongly to economic and technical constraints for the design of new work methods. The most important crop operation in sweet pepper cultivation, harvesting, was pre-modelled in IDEF3 process analysis. The mathematical structure of the GWorkS model is described, as well as specific model adaptations for sweet pepper and inputs determined from labour registration data and video recordings at a sweet pepper grower. Data were analysed for two growers producing different pepper cultivars. Model simulations were performed for one grower. Dynamic simulation results were used to derive technical and economic requirements as numerical constraints for the design of work method innovation.

Construction of the Kalman Filter Algorithm on the Model Reduction

In this paper we derive a state variable estimation method of discrete stochastic dynamical systems. It aims to obtain accurate estimation with short computing time. Therefore, the point of this paper is to discuss a construction of Kalman filter algorithm on the reduced model. First, we construct a reduced model by using balanced truncation method. Further, we apply state variable estimation steps of discrete stochastic dynamical systems by using Kalman filter on the reduced model. Thus, Kalman filter algorithm will be constructed on the reduced model.

Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

A Test for Comparing Two Discrete Stochastic Dynamical Systems Under Heteroskedasticity

In this paper we develop a statistic test in order to compare two discrete stochastic dynamical systems with autoregressive structures under heteroskedasticity, more specifically the variance of the errors follows a general function depending on time. The random disturbances or errors can also be contemporaneously correlated through some structure varying in time. The approach is based on a Wald test and we present three consistent estimates for the asymptotic covariance matrix. The study of the asymptotic properties is based on the Lp-mixingale processes theory since we consider errors generated from martingale difference processes. In order to evaluate the performance of the test in finite samples, we ran some simulations with satisfactory results. A real application is also provided.

An algorithm for identification and computer visualization of events I

A constructive algorithm for processing and identifying events of arbitrary nature is proposed. Ideologically, this algorithm is based on combination of two known approaches: fuzzy sets theory (the fact that the event is “typical” or “untypical” is determined by the value of its membership degree) and the method of potential functions (the metric properties of events are determined with the help of a symmetric nonnegative kernel given by one or another method). From the theoretical point of view, this is an adaptive learning algorithm that makes it possible to identify the analyzed events, and, from the practical point of view, this is an algorithm that gives an opportunity to estimate simultaneously the degree of “typicality”, to calculate the coordinates, to provide computer visualization of these events. The role of events is played by elements of a sequence of output signals of an arbitrary discrete stochastic dynamic system. In addition, the estimation of the “typicality” of events can be considered as the quantitative analysis of the studied system, while the visualization can be considered as its qualitative analysis.

Sensitivity Analysis of Discrete Stochastic Systems

Sensitivity analysis quantifies the dependence of system behavior on the parameters that affect the process dynamics. Classical sensitivity analysis, however, does not directly apply to discrete stochastic dynamical systems, which have recently gained popularity because of its relevance in the simulation of biological processes. In this work, sensitivity analysis for discrete stochastic processes is developed based on density function (distribution) sensitivity, using an analog of the classical sensitivity and the Fisher Information Matrix. There exist many circumstances, such as in systems with multistability, in which the stochastic effects become nontrivial and classical sensitivity analysis on the deterministic representation of a system cannot adequately capture the true system behavior. The proposed analysis is applied to a bistable chemical system—the Schlögl model, and to a synthetic genetic toggle-switch model. Comparisons between the stochastic and deterministic analyses show the significance of explicit consideration of the probabilistic nature in the sensitivity analysis for this class of processes.

Probability-theoretical analog of the vector lyapunov function method

The main ideas of the vector Lyapunov function (VLF) method were advanced in 1962 by Bellman and Matrosov. In this method, a Lyapunov function and a comparison equation are constructed for each subsystem. Then the dependences between the subsystems and the effect of external noise are allowed for by constructing a vector Lyapunov function (as a collection of the scalar Lyapunov functions of the subsystems) and an aggregate comparison function for the entire complex system. A probability-theoretical analog of this method for convergence analysis of stochastic approximation processes has been developed. The abstract approach proposed elsewhere eliminates all restrictions on the system phase space, the system trajectories, the class of Lyapunov functions, etc. The analysis focuses only on the conditions that relate sequences of Lyapunov function values with the derivative and ensure a particular type (mode, character) of stability. In our article, we extend this approach to the VLF method for discrete stochastic dynamic systems.

Detection and estimation for abruptly changing systems

The problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered. The switchings are modelled by a Markov chain with known transition probabilities. A brief survey and a unified treatment of the existing suboptimal algorithms are provided. The optimal algorithms require exponentially increasing memory and computations with time. Simulation results comparing the various suboptimal algorithms are presented.