Non-monotonic changes and bifurcations in the period of coupled BVP oscillators due to noise and cyclic input

Effects of noise and cyclic input on the period of coupled Bonhoeffer-van der Pol (BVP) oscillators are studied with computer simulation. When the noise and cyclic input are added to a fast variable of a single BVP oscillator, the mean oscillation period is monotonically decreased as the strength of noise and the amplitude of input. When two oscillators are linearly coupled and the noise and cyclic input are added to the first oscillator, the periods of the oscillators are changed in qualitatively different manners. The mean and standard deviation of the period of the second oscillator are changed non-monotonically as the strength of the added noise increases. Further, complicated bifurcations in the periods of the oscillators are caused by the cyclic input of small period. Effects of the coupling on the small rotations due to the noise and the cease of the oscillation due to the cyclic input are also studied when the equilibrium point is close to the critical point. The non-monotonic changes and bifurcations in the oscillation period are attributed to the phase locking of the coupled oscillators.