A passivity-based stability criterion for reaction diffusion systems with interconnected structure

Liming Wang

doi:10.3934/dcdsb.2012.17.303

Article Contents

2012, Volume 17, Issue 1: 303-323. Doi: 10.3934/dcdsb.2012.17.303

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A passivity-based stability criterion for reaction diffusion systems with interconnected structure

Liming Wang^1,

1.
Department of Mathematics, California State University, 5151 State University Dr., Los Angeles, CA 90032-8204

Received: April 30, 2010

Revised: March 31, 2011

Published: December 2011

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Abstract

In this paper, stability of a class of reaction diffusion systems is studied. Conditions on global asymptotic stability of the homogeneous equilibrium are derived based on the diagonal stability of a dissipativity matrix. This work extends previous result on global asymptotic stability from cyclic systems to general systems with interconnected structure. In addition, it reformulates the approach using an "input-output" formalism that makes the results easier to understand and apply. A biological example from the Mitogen-Activated Protein Kinase (MAPK) system is provided at the end to illustrate the new approach and the main result.

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Mathematics Subject Classification: 35K57, 93D20, 93D30.

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