Nonmonotone systems decomposable into monotone systems with negative feedback

G. A. Enciso, Hal Smith, E. D. Sontag

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

Motivated by the work of Angeli and Sontag [Monotone control systems, IEEE Trans. Automat. Control 48 (2003) 1684-1698] and Enciso and Sontag [On the global attractivity of abstract dynamical systems satisfying a small gain hypothesis, with applications to biological delay systems, Discrete Continuous Dynamical Systems, to appear] in control theory, we show that certain finite and infinite dimensional semi-dynamical systems with "negative feedback" can be decomposed into a monotone "open-loop" system with "inputs" and a decreasing "output" function. The original system is reconstituted by "plugging the output into the input". Employing a technique of Gouzé [A criterion of global convergence to equilibrium for differential systems with an application to Lotka-Volterra systems, Rapport de Recherche 894, INRIA] and Cosner [Comparison principles for systems that embed in cooperative systems, with applications to diffusive Lotka-Volterra models, Dynam. Cont., Discrete Impulsive Systems 3 (1997) 283-303] of imbedding the system into a larger symmetric monotone system, we are able to obtain information on the asymptotic behavior of solutions, including existence of positively invariant sets and global convergence.

Original languageEnglish (US)
Pages (from-to)205-227
Number of pages23
JournalJournal of Differential Equations
Volume224
Issue number1
DOIs
StatePublished - May 1 2006

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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