The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 111–126 | Cite as

Aspects of stochastic resonance in reaction–diffusion systems: The nonequilibrium-potential approach

  • H. S. WioEmail author
  • R. R. Deza


We analyze several aspects of the phenomenon of stochastic resonance in reaction–diffusion systems, exploiting the nonequilibrium potential's framework. The generalization of this formalism (sketched in the appendix) to extended systems is first carried out in the context of a simplified scalar model, for which stationary patterns can be found analytically. We first show how system-size stochastic resonance arises naturally in this framework, and then how the phenomenon of array-enhanced stochastic resonance can be further enhanced by letting the diffusion coefficient depend on the field. A yet less trivial generalization is exemplified by a stylized version of the FitzHugh–Nagumo system, a paradigm of the activator–inhibitor class. After discussing for this system the second aspect enumerated above, we derive from it–through an adiabatic-like elimination of the inhibitor field–an effective scalar model that includes a nonlocal contribution. Studying the role played by the range of the nonlocal kernel and its effect on stochastic resonance, we find an optimal range that maximizes the system's response.


European Physical Journal Special Topic Noise Intensity Stochastic Resonance Nonlocal Term Stochastic Resonance Phenomenon 
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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Instituto de Física de Cantabria, Universidad de Cantabria and CSICSantanderSpain
  2. 2.Departamento de Física, FCEyNUniversidad Nacional de Mar del Plata Deán Funes 3350Mar del PlataArgentina

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