Displaying 41 – 60 of 109

Showing per page

Finite-time synchronization of chaotic systems with noise perturbation

Jie Wu, Zhi-cai Ma, Yong-zheng Sun, Feng Liu (2015)

Kybernetika

In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical...

Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

N.U. Ahmed (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.

Invariant measures related with randomly connected Poisson driven differential equations

Katarzyna Horbacz (2002)

Annales Polonici Mathematici

We consider the stochastic differential equation (1) d u ( t ) = a ( u ( t ) , ξ ( t ) ) d t + Θ σ ( u ( t ) , θ ) p ( d t , d θ ) for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup P t t 0 corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup P t t 0 describing the evolution of measures along trajectories and vice versa.

Kermack-McKendrick epidemic model revisited

Josef Štěpán, Daniel Hlubinka (2007)

Kybernetika

This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale N t that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size N t . Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer...

Measuring the Irreversibility of Numerical Schemes for Reversible Stochastic Differential Equations

Markos Katsoulakis, Yannis Pantazis, Luc Rey-Bellet (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility...

Currently displaying 41 – 60 of 109