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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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##### References:
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