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Homogeneous Systems with a Quiescent Phase

Published online by Cambridge University Press:  23 October 2008

K. P. Hadeler
K. P. Hadeler*
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
*
hadeler@uni-tuebingen.de
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Abstract

Recently the effect of a quiescent phase (or dormant/resting phase in applications) onthe dynamics of a system of differential equations has been investigated, in particular with respectto stability properties of stationary points. It has been shown that there is a general phenomenonof stabilization against oscillations which can be cast in rigorous form. Here we investigate, forhomogeneous systems, the effect of a quiescent phase, and more generally, a phase with slowerdynamics. We show that each exponential solution of the original system produces two exponentialsolutions of the extended system whereby the stability properties can be controlled.

Keywords

quiescencehomogeneous systemexponential solutionstabilitynon-linear eigenvalueproblempredator-prey system
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 7: Special issue dedicated to Glenn Webb , 2008 , pp. 115 - 125
Copyright
© EDP Sciences, 2008

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