Awakening dynamics via passive coupling and synchronization mechanism in oscillatory cellular neural/nonlinear networks

Abstract We have studied synchronization mechanism in locally coupled nonlinear oscillators. Here, synchronization takes place by passive coupling based on a reaction–diffusion process. We will compare this mechanism with basic synchronization techniques, showing their similarities and specific properties. In addition to synchronization, passive and local coupling can also ‘awaken’ non‐oscillating cell circuits and trigger oscillation, provided that cells are locally active. This result resembles Turing's and Smale's works showing that locally communicating simple elements can produce very different patterns even if separate elements do not show any activity. This property will be demonstrated for two second‐order cells and also for a large ensemble of oscillatory cells. In latter case, the network of oscillatory cells exhibits very sophisticated spatio‐temporal waves, e.g. spiral waves. Copyright © 2008 John Wiley & Sons, Ltd.