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.