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Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity. (English) Zbl 0777.92003
Summary: Three patterns of burst generation and chaos mechanism have been presented in the Rose-Hindmarsh model [J. L. Hindmarsh and R. M. Rose, Nature, Lond. 296, 162-164 (1982), and Proc. R. Soc. Lond., Ser. B 221, 87-102 (1984)] for different parameter regions. We describe the fourth burst pattern exhibited in the model for \(I\leq 2.3\), and obtain the bifurcation portrait for this model over parameter space. The portrait gives a qualitative explanation of burst generation and chaotic mechanism, and provides a qualitative representation how the system evolves over the parameter space.

MSC:
92C20 Neural biology
92-08 Computational methods for problems pertaining to biology
37N99 Applications of dynamical systems
34C23 Bifurcation theory for ordinary differential equations
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