Stability analysis for continuous-time switched systems with stochastic switching signals

This paper is concerned with the stability problem of randomly switched systems. By using the probability analysis method, the almost surely globally asymptotical stability and almost surely exponential stability are investigated for switched systems with semi-Markovian switching, Markovian switching and renewal process switching signals, respectively. Two examples are presented to demonstrate the effectiveness of the proposed results, in which an example of consensus of multi-agent systems with nonlinear dynamics is taken into account

Studying mean-square stability of numerical method applied for solving models of stochastic differential equations

In this paper, Herimte approximations with two collocation points are used for the numerical simulation of stochastic of differential equations (SDE), and continuous wiener processes are computed by computer discrete simulations.  The mean-square stability was studied by applying the proposed technique with the Wiener process on a test stochastic differential equation. The study shows that the proposed method is mean-square stability, strongly convergent from order third and locates large stability regions of method at the real plane. Moreover, the scheme is tested on three problems to illustrate the applicability and efficiency of the purposed technique. Comparisons of our results with others methods, it reveals that our method is better than others.  

Studying mean-square stability of numerical method applied for solving models of stochastic differential equations

In this paper, Herimte approximations with two collocation points are used for the numerical simulation of stochastic of differential equations (SDE), and continuous wiener processes are computed by computer discrete simulations.  The mean-square stability was studied by applying the proposed technique with the Wiener process on a test stochastic differential equation. The study shows that the proposed method is mean-square stability, strongly convergent from order third and locates large stability regions of method at the real plane. Moreover, the scheme is tested on three problems to illustrate the applicability and efficiency of the purposed technique. Comparisons of our results with others methods, it reveals that our method is better than others.  

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems