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Enhancing synchrony in chaotic oscillators by dynamic relaying

Ranjib Banerjee, Dibakar Ghosh, E. Padmanaban, R. Ramaswamy, L.M. Pecora, Syamal Dana
In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when there is a parameter mismatch with the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the central oscillator. We call this lowering of coupling threshold of synchrony as the enhancing effect. In fact, a common time lag is created between the identical outer oscillators and the mismatched central oscillator leading to a LS scenario at a lower critical coupling. This time lag played a role of dynamic relaying in the outer oscillators to establish an indirect coupling via dynamic relaying and thereby enhances CS in the outer oscillators. We present several example systems to verify the LS scenario causing the enhancing effect both in presence and in absence of coupling delay. We confirm the effect in Lorenz and Rössler systems in absence of coupling delay and in the Mackey-Glass system with coupling delay. The effect is also observed in a chain of Hindmarsh-Rose bursting oscillators and thus appears to be a general effect in nonlinear dynamical systems since a parameter regime of LS scenario can always be found in chaotic systems. We provide experimental evidence of the LS scenario and the enhancing effect using electronic circuit of Rössler oscillators. An enhancing of synchrony was reported earlier in two oscillators by an induced coupling delay when the coupled system switches from a chaotic to a periodic state. But, in our case, the coupled oscillators remain chaotic before and after coupling. The enhancing effect is also true for a negative mismatch where the central oscillator leads the outer ones instead of lagging.
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