Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity

Abstract Three patterns of burst generation and chaos mechanism have been presented in the Rose-Hindmarsh model for different parameter regions. In the present paper, we describe the fourth burst pattern exhibited in the model for I ⩽ 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.

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