Some aspects of the synchronization in coupled maps

Abstract

Through numerical simulations we analyze the synchronization time and the Lyapunov dimension of a coupled map lattice consisting of a chain of chaotic logistic maps exhibiting power law interactions. From the observed behaviors we find a lower bound for the size $N$ of the lattice, independent of the range and strength of the interaction, which imposes a practical lower bound in numerical simulations for the system to be considered in the thermodynamic limit. We also observe the existence of a strong correlation between the averaged synchronization time and the Lyapunov dimension. This is an interesting result because it allows an analytical estimation of the synchronization time, which otherwise requires numerical simulations.

4 pages, 6 figures

References in corpus (6)

• Delays, connection topology, and synchronization of coupled chaotic maps
• Spectral Properties and Synchronization in Coupled Map Lattices
• Coherence in scale-free networks of chaotic maps
• Analytical results for coupled map lattices with long-range interactions
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Cited by in corpus (2)

• Critical parameters of the synchronisation's stability for coupled maps in regular graphs
• Synchronization time in a hyperbolic dynamical system with long-range interactions