Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633714 | Applied Mathematics and Computation | 2009 | 8 Pages |
Abstract
This paper deals with the stability problem of a delay differential system of the form x′(t)=-ax(t-τ)-by(t)x′(t)=-ax(t-τ)-by(t), y′(t)=-cx(t)-ay(t-τ)y′(t)=-cx(t)-ay(t-τ), where a, b, and c are real numbers and ττ is a positive number. We establish some necessary and sufficient conditions for the zero solution of the system to be asymptotically stable. In particular, as ττ increases monotonously from 0, the zero solution of the system switches finite times from stability to instability to stability if 0<4a<-bc; and from instability to stability to instability if --bc<2a<0. As an application, we investigate the local asymptotic stability of a positive equilibrium of delayed Lotka–Volterra systems.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hideaki Matsunaga,