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Simple Stability Criteria for a Nonlinear Nonautonomous System With Delays With Application to Marine Protected Areas Models
by
Lev Idels
Department of Mathematics , Malaspina University, Nanaimo, BC, Canada
Coauthors: M. Kipnis
This paper further develops a method, originally introduced by T. Mori, for proving local stability of steady states in linear systems of delay differential equations. A nonlinear nonautonomous system of delay differential equations with several delays is considered. Explicit delay-independent sufficient conditions for global attractivity of the solutions with an extremely simple form are provided. The above-mentioned conditions make the stability test quite practical. The results obtained were applied to the marine protected areas model with delay that describes the ecological linkage between the reserve and fishing ground. It is shown the extinction of population under excessive harvesting
Date received: January 31, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-92.