Stability of Equilibria of Some Models of Rumor and Information Spreading under Stochastic Perturbations | Chapter 9 | Research Highlights in Mathematics and Computer Science Vol. 9

 This affiliate is devoted to cohesion investigation of two mathematical models of rumor and facts spreading. The numerical model of rumor spreading is described by a arrangement of four nonlinear differential equatings, the nonlinear discrete-time model of facts dissemination is characterized by a system of three dissimilarity equations. Equilibria of each system are outlined and it is supposed that the thought-out model is influenced by stochastic perturbations of the various types that are proportional to the change of the system state from one of allure equilibrium. Sufficient environments of stability in possibility for each from the equilibria of the considered model are got via the Routh-Hurwitz test, the Lyapunov functions method and the method of undeviating matrix prejudices (LMIs). The obtained results are pictorial by numerical analysis of appropriate LMIs by way of MATLAB and numerical simulations of resolutions of the considered system of theory of probability differential or dissimilarity equations. An unsolved question is proposed in the second place the presented analyses. The research method used attending can be used to investigate many other differing applications for complementary nonlinear mathematical models with an order of nonlinearity above one.

\Author(s) Details:

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

Please see the link here: https://stm.bookpi.org/RHMCS-V9/article/view/10416

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

A Survey of Some Applications of One Method of Stability Investigation under Stochastic Perturbations| Chapter 1 | Research Highlights in Mathematics and Computer Science Vol. 3

 A survey of use of the method of security investigation of equilibria in different used mathematical models under theory of probability perturbations is presented.

Author(s) Details:

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

Please see the link here: https://stm.bookpi.org/RHMCS-V3/article/view/8873

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

Stability of Equilibria of Stochastically Perturbed Nonlinear Mathematical Models| Chapter 5 | Research Highlights in Mathematics and Computer Science Vol. 1

 The Smooth winged Sharpshooter's realized nonlinear numerical model is thought about. This model is believed to be impacted by stochastic bothers of the background noise, and these irritations are believed to be precisely corresponding to the framework state's deviation from the positive harmony. We get a vital and adequate condition for the harmony of the straight part of the nonlinear stochastic differential condition viable to have asympt-otic mean square steadiness. This need is likewise an adequate one for the likelihood based strength of the harmony of the underlying nonlinear condition. The outcomes are displayed in mathematical calculations and figures. It is noticed that the motivation behind this exploration isn't to concentrate on the solidness of a specific model. The proposed technique for strength examination can be applied to concentrate on steadiness of numerous other nonlinear conditions and frameworks of nonlinear conditions under stochastic annoyances.

Author(s) Details:

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

Please see the link here: https://stm.bookpi.org/RHMCS-V1/article/view/8244