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Phase-flip bifurcation plays an important role in the transition tosynchronization state in unidirectionally coupled parametrically excitedpendula. In coupled identical system it is the cause of completesynchronization whereas in case of coupled non-identical system it causesdesynchronization. In coupled identical systems negativity of conditionalLyapunov exponent is not always sufficient for complete synchronization. Incomplete synchronization state the largest conditional Lyapunov exponent andthe second largest Lyapunov exponent are equal in magnitude and slope.

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