Crisis-induced chaos in the Rose-Hindmarsh model for neuronal activity

Abstract The bifurcation diagrams for the Rose-Hindmarsh model are obtained from the Poincare maps which govern the dynamics of this differential system. The Lyapunov spectra for this model are estimated from time series. The transition from periodicity to crisis-induced chaos. and back to periodicity is presented for I e [2.5, 2.69]. and is qualitatively different from the transitions described for different parameter regions [A. V. Holden and Yinshui Fan, Chaos, Solitons & Fractals2, 221–236 (1992); Chaos, Solitons & Fractals 2, 349–369 (1992)]. A piecewise smooth, one-dimensional map is constructed to simulate the dynamics of the model and to reproduce the process of crisis-induced chaos.

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