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Henning D. ., Sailer F. X., Schimansky-Geier L. . Patterns in excitable dynamics driven by additive dichotomic noise. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 4, pp. 49-63. DOI: 10.18500/0869-6632-2009-17-4-49-63

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Patterns in excitable dynamics driven by additive dichotomic noise

Henning Dirk , University of Portsmouth
Sailer Franz Xaver Xaver, University of Portsmouth
Schimansky-Geier Lutz , University of Portsmouth

Pattern formation due the presence of additive dichotomous fluctuations is studied an extended system with diffusive coupling and a bistable FitzHugh–Nagumo kinetics. The fluctuations vary in space and/or time being noise or disorder, respectively. Without perturbations the dynamics does not support pattern formation. With proper dichotomous fluctuations, however, the homogeneous steady state is destabilized either via a Turing instability or the fluctuations create spatial nuclei of an inhomogeneous states. Finally, for purely static dichotomous disorder we find destabilization of homogeneous steady states for finite nonzero correlation length of the disorder resulting again in spatial patterns.

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