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Nonlocal control of pulse propagation in excitable media

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  • Clemens Bachmair
  • Eckehard Schöll

Abstract

We study the effects of nonlocal control of pulse propagation in excitable media. As a generic example for an excitable medium the FitzHugh-Nagumo model with diffusion in the activator variable is considered. Nonlocal coupling in form of an integral term with a spatial kernel is added. We find that the nonlocal coupling modifies the propagating pulses of the reaction-diffusion system such that a variety of spatio-temporal patterns are generated including acceleration, deceleration, suppression, or generation of pulses, multiple pulses, and blinking pulse trains. It is shown that one can observe these effects for various choices of the integral kernel and the coupling scheme, provided that the control strength and spatial extension of the integral kernel is appropriate. In addition, an analytical procedure is developed to describe the stability borders of the spatially homogeneous steady state in control parameter space in dependence on the parameters of the nonlocal coupling. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Clemens Bachmair & Eckehard Schöll, 2014. "Nonlocal control of pulse propagation in excitable media," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(11), pages 1-10, November.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:11:p:1-10:10.1140/epjb/e2014-50339-2
    DOI: 10.1140/epjb/e2014-50339-2
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    Cited by:

    1. Peter Nestler & Eckehard Schöll & Fredi Tröltzsch, 2016. "Optimization of nonlocal time-delayed feedback controllers," Computational Optimization and Applications, Springer, vol. 64(1), pages 265-294, May.

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    Statistical and Nonlinear Physics;

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