Random coupling of chaotic maps leads to spatiotemporal synchronization

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Coupled chaotic maps exhibit complex spatiotemporal dynamics.
• Nearest neighbor coupling typically prevents synchronization in such systems.
• Understanding the role of network topology in chaotic systems is crucial.

Purpose of the Study:

• To investigate how varying degrees of randomness in coupling connections affect spatiotemporal synchronization in chaotic map networks.
• To identify the conditions under which random rewiring can stabilize the network dynamics.
• To analyze the scaling behavior of synchronization onset with the fraction of random connections.

Main Methods:

• Simulations of coupled chaotic maps with controlled rewiring of connections.
• Analysis of spatiotemporal synchronization and stability of the fixed point.
• Power-law scaling analysis of synchronization onset parameter epsilon(bifr) with rewiring fraction p.
• Stability analysis of the probabilistic evolution equation for the system.

Main Results:

• Strict nearest neighbor coupling does not lead to spatiotemporal synchronization.
• Random rewiring of connections stabilizes the network at the unstable fixed point x*.
• Even small amounts of randomness create a window of stability for the synchronized fixed point.
• The critical coupling epsilon(bifr) for synchronization onset follows a power-law relationship with the rewiring fraction p (0.1

Conclusions:

• Randomness in spatial connections acts as a regularizing mechanism in chaotic map networks.
• The observed stabilization and synchronization are analytically supported by the probabilistic evolution equation.
• Approximate analytical expressions for the stability range and critical coupling were derived.