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Persistent clusters in lattices of coupled nonidentical chaotic systems. (English) Zbl 1080.37525
Summary: Two-dimensional (2D) lattices of diffusively coupled chaotic oscillators are studied. In previous work, it was shown that various cluster synchronization regimes exist when the oscillators are identical. Here, analytical and numerical studies allow us to conclude that these cluster synchronization regimes persist when the chaotic oscillators have slightly different parameters. In the analytical approach, the stability of almost-perfect synchronization regimes is proved via the Lyapunov function method for a wide class of systems, and the synchronization error is estimated. Examples include a 2D lattice of nonidentical Lorenz systems with scalar diffusive coupling. In the numerical study, it is shown that in lattices of Lorenz and Rössler systems the cluster synchronization regimes are stable and robust against up to $10\%-15\%$ parameter mismatch and against small noise.

37D45Strange attractors, chaotic dynamics
34C15Nonlinear oscillations, coupled oscillators (ODE)
34D23Global stability of ODE
82C05Classical dynamic and nonequilibrium statistical mechanics (general)
82C20Dynamic lattice systems and systems on graphs
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