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From simple to simple bursting oscillatory behaviour via chaos in the Rose- Hindmarsh model for neuronal activity. (English) Zbl 0766.92006
Summary: The bifurcation diagrams for the Rose-Hindmarsh model are obtained from the Poincaré maps which govern the dynamics of this differential system. This and a sequence of burst patterns that undergoes transition from simple to simple bursting oscillatory behaviour via chaos are presented. This burst pattern simulates the repetitive, patterned and irregular activity seen in molluscan neurones. Additionally, some maps are used to qualitatively analyze the period-2 chaos exhibited in this system.

MSC:
92C20 Neural biology
34C23 Bifurcation theory for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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