Critical perturbation sizes for preserving decay rates in solutions of perturbed nonlinear differential equations

TL;DR

This paper establishes conditions under which the decay rates of solutions to nonlinear differential equations are preserved when the equations are subjected to deterministic and stochastic perturbations, focusing on power-law decay to zero.

Contribution

It provides necessary and sufficient conditions for maintaining decay rates in perturbed nonlinear differential equations, extending understanding of stability under perturbations.

Findings

Derived conditions for decay rate preservation

Applicable to both deterministic and stochastic perturbations

Enhances stability analysis of nonlinear differential equations

Abstract

This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations in which the solutions of the unperturbed equations exhibit have power--law decay to zero.