Stability tests and solution estimates for non-linear differential equations

Abstract

This article deals with certain systems of delay differential equations (DDEs) and a system of ordinary differential equations (ODEs). Here, five new theorems are proved on the fundamental properties of solutions of these systems. The results on the properties of solutions consist of sufficient conditions and they dealt with uniformly asymptotically stability (UAS), instability and integrability of solutions of unperturbed systems of DDEs, boundedness of solutions of a perturbed system of DDEs at infinity and exponentially stability (ES) of solutions of a system of nonlinear ODEs. Here, the techniques of proofs depend upon the Lyapunov- Krasovski? functional (LKF) method and Lyapunov function (LF) method. For illustrations, in particular cases, four examples are constructed as applications. Some results of this paper are given at first time in the literature, and the other results generalize and improve some related ones in the literature.

Asymptotic Stability of Neutral Differential Systems with Variable Delay and Nonlinear Perturbations

“…The obtained sufficient conditions are presented in terms of either matrix norm or matrix measure operations which by Park and Won [25], are conservative. Other relevant papers on chaotic control and hyperchaotic systems with time delay include Feng et al [26], Onasanya et al [27], stability tests and solution estimates for non-linear differential equations Tunç [28], among others.…”

The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations

“…The examination of catastrophic issues, such as equilibrium points, catastrophic manifold, capacitance, and phenomenon jump, has been of great interest for a long time because of its increasing applications in physical, biological, and social sciences. Some writers, such as [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], and the authors made important contributions to the examination of various topics, such as points of balance, catastrophic models, recurring patterns, stability and instability, and phenomena linked to forced vibrations. This study aims to determine periodic solutions in a non-linear differential equation and assess their stability and semi-stability.…”