Global attractivity, I/O monotone small-gain theorems, and biological delay systems
G. A. Enciso - Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, United States (email)
Abstract: This paper further develops a method, originally introduced by Angeli and the second author, for proving global attractivity of steady states in certain classes of dynamical systems. In this approach, one views the given system as a negative feedback loop of a monotone controlled system. An auxiliary discrete system, whose global attractivity implies that of the original system, plays a key role in the theory, which is presented in a general Banach space setting. Applications are given to delay systems, as well as to systems with multiple inputs and outputs, and the question of expressing a given system in the required negative feedback form is addressed.
Keywords: Monotone systems, negative feedback, global attractivity, delay systems, mathematical biology.
Received: October 2004; Revised: March 2005; Published: December 2005.
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