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Phase synchronization and its cluster feature in two-dimensional coupled map lattices.
GuoCe Zhuang1, Jun Wang, Yi Shi
1National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University, People's Republic of China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
Summary
Phase synchronization emerges in chaotic coupled map lattices. A novel percolation-like transition in direction phases is observed, revealing new synchronization patterns and scaling laws.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Phase synchronization is a key phenomenon in coupled chaotic systems.
- Chaotic coupled map lattices (CCMLs) provide a framework for studying emergent dynamics.
- Understanding pattern formation in spatially extended chaotic systems is crucial.
Purpose of the Study:
- To investigate novel phase synchronization states in 2D chaotic coupled map lattices.
- To analyze the emergence of pattern formation through phase synchronization.
- To characterize the transition dynamics and scaling behavior.
Main Methods:
- Utilizing diffusive nearest-neighbor coupling in a 2D logistic map lattice.
- Defining a 'direction phase' based on sequential map iterations.
- Analyzing phase diagrams, percolation transitions, and correlation functions.
Main Results:
- Identification of four distinct regions of phase synchronization.
- Discovery of a percolation-like transition in direction phase clusters at a critical coupling strength.
- Empirical observation of a scaling law: rho ~ (epsilon - epsilon(c))^2.1.
- Characterization of spatial and temporal correlations within phase clusters.
Conclusions:
- Diffusive coupling in 2D CCMLs can lead to diverse phase-synchronized states.
- The direction phase concept reveals novel synchronization phenomena and pattern formation.
- The observed percolation transition and scaling law offer insights into the collective behavior of chaotic systems.