Coupled Dynamics and Quiescent Phases

Karl P. Hadeler () and Thomas Hillen ()
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Karl P. Hadeler: Universität Tübingen, Germany & Arizona State University
Thomas Hillen: University of Alberta

A chapter in Math Everywhere, 2007, pp 7-23 from Springer

Abstract: Abstract We analyze diffusively coupled dynamical systems, which are constructed from two dynamical systems in continuous time by switching between the two dynamics. If one of the vector fields is zero we call it a quiescent phase. We present a detailed analysis of coupled systems and of systems with quiescent phase and we prove results on scaling limits, singular perturbations, attractors, gradient fields, stability of stationary points and amplitudes of periodic orbits. In particular we show that introducing a quiescent phase is always stabilizing.

Keywords: Periodic Orbit; Singular Perturbation; Global Attractor; Slow Manifold; Outer Solution (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-44446-6_2

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DOI: 10.1007/978-3-540-44446-6_2

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