Bifurcations and chaos of the Bonhoeffer-van der Pol model

Wang, William (1989) Bifurcations and chaos of the Bonhoeffer-van der Pol model. Journal of Physics A: Mathematical and General, 22 (13). L627. ISSN 0305-4470

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Abstract

Periodic and chaotic behaviour of the Bonhoeffer-van der Pol model of a nerve membrane driven by a periodic stimulating current a1 cos omega t is investigated. Results show that there exist ordinary and reversed period-doubling cascades and a mode-locking state. At low driving amplitudes a1, there are period-doubling and chaotic states, but no impulse solutions. When a1 is larger than a0=0.749, there are chaotic, reversed period-doubling, and mode-locking states and there also exist impulse trains. A mode-locking state with period 4 over a very large range of amplitudes is also found. At a1=1.7059 the system goes back to a one-period state.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: William Wang
Date Deposited: 06 Feb 2012 19:02
Last Modified: 02 Jul 2012 11:30
URI: http://sro.sussex.ac.uk/id/eprint/19012
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