Order reprints

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents

Paul L. Salceanu

*Corresponding author:  

MBE2011,3,807doi:10.3934/mbe.2011.8.807

This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence in a class of dissipative discrete-time dynamical systems on the positive orthant of $\mathbb{R}^m$, generated by maps. Here a unified approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of $\mathbb{R}^m_+$ to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.

Please supply your name and a valid email address you yourself

Fields marked*are required

Article URL   http://www.aimspress.com/MBE/article/2619.html
Article ID   1551-0018_2011_3_807
Editorial Email  
Your Name *
Your Email *
Quantity *

Copyright © AIMS Press All Rights Reserved