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Bubbling bifurcation: Loss of synchronization and shadowing breakdown in complex systems. (English) Zbl 1099.37511

In the present study the authors pursued the close correspondence between shadowing breakdown via unstable dimension variability and the intermittent transition to synchronization in a complex system comprised of a coupled map lattice with variable range coupling. A tunable parameter allows the authors to pass continuously from a local (nearest-neighbor) to a global (mean field) coupling. The existence of a transition to synchronization as thus variable range is swept over its interval is a well-established fact, but in this paper the authors focused on the behaviour near criticality.

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
37N05 Dynamical systems in classical and celestial mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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