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Numerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh–Nagumo equation

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  • Ford, Neville J.
  • Lima, Pedro M.
  • Lumb, Patricia M.

Abstract

In this work we introduce and analyse a stochastic functional equation, which contains both delayed and advanced arguments. This equation results from adding a stochastic term to the discrete FitzHugh–Nagumo equation which arises in mathematical models of nerve conduction. A numerical method is introduced to compute approximate solutions and some numerical experiments are carried out to investigate their dynamical behaviour and compare them with the solutions of the corresponding deterministic equation.

Suggested Citation

  • Ford, Neville J. & Lima, Pedro M. & Lumb, Patricia M., 2017. "Numerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh–Nagumo equation," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 448-460.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:448-460
    DOI: 10.1016/j.amc.2016.08.035
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    References listed on IDEAS

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    1. Perc, Matjaž, 2007. "Spatial coherence resonance in neuronal media with discrete local dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 64-69.
    2. Perc, Matjaž, 2007. "Effects of small-world connectivity on noise-induced temporal and spatial order in neural media," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 280-291.
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