Fatihcan M Atay
Articles written in Pramana – Journal of Physics
Volume 77 Issue 5 November 2011 pp 855-863 Synchronization, Coupled Systems and Networks
We show how novel behaviour can emerge in complex systems at the global level through synchronization of the activities of their constituent units. Two mechanisms are suggested for the emergence, namely non-diffusive coupling and time delays. In this way, simple units can synchronize to display complex dynamics, or conversely, simple dynamics may arise from complex constituents.
Volume 77 Issue 5 November 2011 pp 905-915 Synchronization, Coupled Systems and Networks
We investigate phase-locked solutions of a continuum ﬁeld of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and travelling wave solutions in the parameter space characterizing the nonlocality and time delay are delineated. For the synchronous states a comprehensive stability diagram is presented that provides a heuristic synchronization condition as well as an analytic relation for the marginal stability curve. The relation yields simple stability expressions in the limiting cases of local and global coupling of phase oscillators.
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