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Drive–response; response time; distributed delay; synchronization.

The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval 𝜏. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous $(\tau = 0)$ case. The critical coupling strength at which synchronization sets in is found to increase with 𝜏. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization.

Garima Saxena¹ Awadhesh Prasad¹ Ram Ramaswamy^{2 3}

1. Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India
2. School of Physics, Jawaharlal Nehru University, New Delhi 110 067, India
3. University of Hyderabad, Hyderabad 500 046, India

Published

November 2011