Global attractivity, I/O monotone small-gain theorems, and biological delay systems

Pages: 549 - 578, Volume 14, Issue 3, March 2006

doi:10.3934/dcds.2006.14.549       Abstract        Full Text (407.3K)       Related Articles

G. A. Enciso - Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, United States (email)
E. D. Sontag - 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.
Mathematics Subject Classification:  93D25, 92B99, 93C10, 34D23.

Received: October 2004;      Revised: March 2005;      Published: December 2005.