Period-doubling bifurcations, chaos, phase-locking and devil's staircase in a Bonhoeffer-van der Pol oscillator (Q1111213)

The effect of a periodic input current \(A_ 1 \cos t\) in the Bonhoeffer- van der Pol oscillator along with a bias \(A_ 0\) is investigated numerically. As the parameter \(A_ 1\) is varied in the absence of bias by holding the other parameters at constant values, typical period- doubling bifurcation sequence is found to occur leading to chaotic motion in agreement with the Feigenbaum scenario. When the bias is switched on at the transition to chaos, frequency-locking is observed in the system. The frequency-locked intervals exhibit complete devil's staircase similar to the one observed in Belousov-Zhabotinsky reaction.