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Phase-flip bifurcation: Theory and experiment

Syamal Kumar Dana, Juergen Kurths, Ramakrishna Ramaswamy, Awadhesh Prasad
Phase synchronization is common in weakly coupled nonlinear systems. Basically two types of phase synchronization, in-phase and antiphase or out-of-phase are seen in both instantaneously coupled and delay coupled systems. A transition to either of the synchronization states can be induced by changing the coupling strength in instantaneously coupled systems or by changing delay time in delay coupled systems. However, the transition from inphase to antiphase state or vice versa is found intercepted by a desynchronization regime in instantaneously coupled systems. On the contrary, a sharp transition from inphase to antiphase is observed in two delay coupled oscillators when the time delay is varied above a critical value. This phenomenon of sharp transition from inphase to antiphase with time delay is defined as phase-flip bifurcation. The phase-flip is accompanied by a large change in oscillator frequency from a lower to higher value respectively. We describe here our results both theoretical and experimental on phase-flip bifurcation. First we present the theoretical framework of phase-flip bifurcation using two identical Rössler oscillators and then its experimental evidence in electronic circuit of two delay coupled Chua oscillators.
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