A Study on Mathematical Modeling, Difference, Linear and Non-Linear Equations

Stability and Behavior of Differential Equations under Stochastic Perturbations

Abstract

We portray the worldwide asymptotic steadiness of the novel balance of a scalar deterministic customary differential equation when it is subjected to a stochastic annoyance free of the state. Another real undertaking is to order the asymptotic conduct of arrangements into concurrent, intermittent or limited under some more grounded mean returning condition on the nonlinearity. What is of uncommon intrigue is that, in the previous case, arrangements will be universally joined under the very same conditions on the force of the stochastic bother σ that apply in the straight case, and to be sure, these conditions which guarantee soundness are completely free of the kind of nonlinear mean inversion not at all like the deterministic case we don't have to make any presumption on the quality of the mean– inversion, simply that it is constantly present.