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From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity. (English) Zbl 0753.92009
Summary: The Rose-Hindmarsh equations [see J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. Lond., Ser. B 221, 87-102 (1984)] are a system of three nonlinear ordinary differential equations that provide a phenomenological model for repetitive, patterned and irregular activity in molluscan neurons. We obtain bifurcation diagrams for this system, and obtain interval maps that reproduce the behaviour of the differential system. These maps are used to explore the bifurcations from simple to complex oscillatory behaviour.

MSC:
92C20 Neural biology
34C23 Bifurcation theory for ordinary differential equations
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