Excitability in a Model with a Saddle-Node Homoclinic Bifurcation

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dc.creatorDilao, Rui
dc.creatorVolford, Andras
dc.date2005-02-25
dc.date.accessioned2026-07-07T04:31:54Z
dc.date.available2026-07-07T04:31:54Z
dc.descriptionIn order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node homoclinic bifurcation as observed in chemical experiments, and for the concepts of excitability and excitability threshold. We show that if diffusion drives an extended system across the excitability threshold then, depending on the initial conditions, wave trains, propagating solitary pulses and propagating pulse packets can exist in the same extended system. The extended model shows chemical turbulence for equal diffusion coefficients and presents all the known types of topologically distinct activity waves observed in chemical experiments. In particular, the approach presented here enables to design experiments in order to decide between excitable systems with sharp and finite width thresholds.
dc.description18 pages, 7 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0502049
dc.identifierhttp://arxiv.org/abs/math-ph/0502049
dc.identifierDCDS, vol 4 (2004) 419-434
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57989
dc.subjectMathematical Physics
dc.subject45K57
dc.titleExcitability in a Model with a Saddle-Node Homoclinic Bifurcation
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