Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback

Preprint

20 December 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0112232

Abstract

The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly feedback-dependent, steady states. A Lyapunov-like characterization allows the computation of gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops. An application in biology (MAPK signaling) is worked out in detail.

Keywords

ASYMPTOTIC AMPLITUDE
SMALL GAIN PRINCIPLE
CAUCHY GAIN
FEEDBACK
BIOLOGY
MAPK

All Related Versions

Version 1, 2001-12-20, ArXiv

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