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Coupled Dynamics and Quiescent Phases

In: Math Everywhere

Author

Listed:
  • Karl P. Hadeler

    (Universität Tübingen, Germany & Arizona State University)

  • Thomas Hillen

    (University of Alberta)

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.

Suggested Citation

  • Karl P. Hadeler & Thomas Hillen, 2007. "Coupled Dynamics and Quiescent Phases," Springer Books, in: Giacomo Aletti & Alessandra Micheletti & Daniela Morale & Martin Burger (ed.), Math Everywhere, pages 7-23, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-44446-6_2
    DOI: 10.1007/978-3-540-44446-6_2
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