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Stochastic synchronization in blinking networks of chaotic maps
1Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University Brooklyn, 11201, USA. mporfiri@poly.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study analyzes stochastic synchronization in chaotic maps on dynamic networks. We derived a condition for synchronization stability using network properties and chaos theory, confirmed with Henon map simulations.
Area of Science:
- Complex Systems
- Network Science
- Chaos Theory
Background:
- Coupled chaotic systems exhibit complex dynamics.
- Network structure significantly impacts synchronization phenomena.
- Stochasticity and dynamic network topologies introduce challenges in analyzing synchronization.
Purpose of the Study:
- To analyze the stochastic synchronization of coupled chaotic maps on blinking networks.
- To establish a necessary and sufficient condition for the mean square linear stability of the synchronized state.
- To investigate the influence of network topology and stochastic couplings on synchronization.
Main Methods:
- Analysis of the time evolution of the second moment of variation transverse to the synchronization manifold.
- Projection of variational equations onto eigenvectors of the state matrix.
- Derivation of a synchronization condition based on Lyapunov exponents and spectral radius.
- Computation of spectral properties of graph Laplacian moments for intermittent couplings.
Main Results:
- A necessary and sufficient condition for stochastic synchronization was established.
- The condition links synchronization stability to the largest Lyapunov exponent and spectral radius of the state matrix.
- Closed-form results for spectral properties of the graph Laplacian moments were derived.
- Simulations confirmed the theoretical findings using chaotic Henon maps.
Conclusions:
- The study provides a robust analytical framework for understanding stochastic synchronization in dynamic networks.
- The derived condition offers a powerful tool for predicting and controlling synchronization in complex systems.
- The findings are applicable to various fields involving coupled chaotic oscillators and network dynamics.
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