Global attractivity for nonlinear differential equations with a nonlocal term

Abstract

In this article we analyze the dynamics of the problem $$\displaylines{ x'(t)=-(\delta+\beta(x(t)))x(t)+\theta\int_{0}^{\tau}f(a)x(t-a)\beta(x(t-a))da, \quad t> \tau, \cr x(t)=\phi(t),\quad 0 \leq t\leq \tau, }$$ where $\delta,\theta$ are positive constants, and $\beta, \phi, f$ are positives continuous functions. The main results obtained in this paper are the following:

Keywords

• Global stability
• Lyapunov function
• asymptotic analysis
• Laplace transform, Nicholson's blowflies model