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An alternative bifurcation analysis of the Rose–Hindmarsh model

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  • Nikolov, Svetoslav

Abstract

The paper presents an alternative study of the bifurcation behavior of the Rose–Hindmarsh model using Lyapunov–Andronov’s theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov’s value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose–Hindmarsh system take place under hard stability loss.

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  • Nikolov, Svetoslav, 2005. "An alternative bifurcation analysis of the Rose–Hindmarsh model," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1643-1649.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:5:p:1643-1649
    DOI: 10.1016/j.chaos.2004.06.080
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    Cited by:

    1. Hou, Zhangliang & Ma, Jun & Zhan, Xuan & Yang, Lijian & Jia, Ya, 2021. "Estimate the electrical activity in a neuron under depolarization field," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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