Unpredictability of the asymptotic attractors in phase-coupled oscillators.

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An array of phase-coupled oscillators may exhibit multiple coexisting chaotic and nonchaotic attractors. The system of coupled circle maps is such an example. We demonstrate that it is common for this type of system to exhibit an extreme type of final state sensitivity in both parameter and phase space. Numerical computations reveal that there exist substantial regions of the parameter space where arbitrarily small perturbations in parameters or initial conditions can alter the asymptotic attractor of the system completely. Consequently, asymptotic attractors of the system cannot be predicted reliably for specific parameter values and initial conditions.