Phase-flip bifurcation and synchronous transition in unidirectionally coupled parametrically excited pendula

Abstract: Phase-flip bifurcation plays an important role in the transition to synchronization state in unidirectionally coupled parametrically excited pendula. In coupled identical system it is the cause of complete synchronization whereas in case of coupled non-identical system it causes desynchronization. In coupled identical systems negativity of conditional Lyapunov exponent is not always sufficient for complete synchronization. In complete synchronization state the largest conditional Lyapunov exponent and the second largest Lyapunov exponent are equal in magnitude and slope.