Stability of Stochastic Differential Equations with State-dependent Delays | Chapter 4 | Research Highlights in Mathematics and Computer Science Vol. 7

 This branch is devoted to stability case of systems accompanying state-dependent delays under stochastic perturbations. Sufficient environments of asymptotic mean square stability for the nothing solution of a linear theory of probability differential equation accompanying distributed delays are acquired via the general form of Lyapunov functionals construction and the plan of linear matrix prejudices (LMIs). Besides delay-independent and delay-dependent environments of stability in odds are obtained for two equilibria of a nonlinear stochastic characteristic equation unhurriedly and exponential nonlinearity. The negative definiteness of casts in the obtained LMIs is checked utilizing the special MATLAB program. It is eminent that the proposed research method maybe used for the study of additional types of linear and nonlinear systems accompanying state-dependent delays. Numerical simulation of resolutions of the considered theory of probability differential equations accompanying state-dependent delays represent the presented here hypothetical results and open to readers consideration a new unsolved question of the obtained stability environments improving.

Author(s) Details:

Leonid Shaikhet,
Department of Mathematics, Ariel University, Ariel 40700, Israel.

Please see the link here: https://stm.bookpi.org/RHMCS-V7/article/view/9998

Stability Investigation of Systems of Nonlinear Stochastic Difference Equations| Chapter 6 | Research Highlights in Mathematics and Computer Science Vol. 2

 The aim concerning this research is to present a method for establishment investigation of systems of nonlinear distinctness equations influenced by various types of stochastic perturbations. The projected method is demonstrated on the strength investigation of a nonlinear discrete-opportunity model of information dissemination. We get the conditions for this system's certain equilibrium. It is demonstrated that drunk of stochastic perturbations of the various forms, containing minor multiplicative perturbations, rapidly fading multiplicative perturbations, and promptly fading preservative perturbations, asymptotically stable positive balance maintains its balance. Through the use of Lyapunov functions, linear matrix prejudices (LMIs), and numerical simulations of the system existing, stability requirements are driven. It is suggested to look at the synopsis where stochastic disturbances dissolve on the infinity, but not very fast, as an unresolved problem. The deliberate here method of strength investigation can be used for many other nonlinear mathematical models interpreted both by stochastic dissimilarity equations and by stochastic characteristic equations.

Author(s) Details:

Leonid Shaikhet,
Department of Mathematics, Ariel University, Ariel-40700, Israel.

Please see the link here: https://stm.bookpi.org/RHMCS-V2/article/view/8573