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• W3131381188 abstract "In this chapter we consider the invariant method for stochastic system with strong perturbations, and its application to many different tasks related to dynamical systems with invariants. This theory allows constructing the mathematical model (deterministic and stochastic) of actual process if it has invariant functions. These models have a kind of jump-diffusion equations system (stochastic differential Itô equations with a Wiener and a Poisson paths). We show that an invariant function (with probability 1) for stochastic dynamical system under strong perturbations exists. We consider a programmed control with Prob. 1 for stochastic dynamical systems – PSP1. We study the construction of stochastic models with invariant function based on deterministic model with invariant one and show the results of numerical simulation. The concept of a first integral for stochastic differential equation Itô introduce by V. Doobko, and the generalized Itô – Wentzell formula for jump-diffusion function proved us, play the key role for this research." @default.
• W3131381188 created "2021-03-01" @default.
• W3131381188 creator A5033641905 @default.
• W3131381188 date "2021-07-28" @default.
• W3131381188 modified "2023-10-18" @default.
• W3131381188 title "Invariants for a Dynamical System with Strong Random Perturbations" @default.
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• W3131381188 doi "https://doi.org/10.5772/intechopen.96235" @default.
• W3131381188 hasPublicationYear "2021" @default.
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