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Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
D V Senthilkumar1, P Muruganandam, M Lakshmanan
1Centre for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Researchers enhanced chaos synchronization in coupled nonlinear oscillators by adding specific couplings. This method significantly increases the number of synchronized oscillators beyond previous limits, improving system stability and robustness against noise.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Chaos synchronization in diffusively coupled nonlinear oscillators is crucial for understanding complex system behavior.
- Previous studies were limited by size instability, restricting the number of synchronized oscillators.
Purpose of the Study:
- To investigate methods for increasing the number of synchronized oscillators in a ring network.
- To analyze the relationship between coupling strength, number of oscillators, and synchronization stability.
- To examine the robustness of synchronization against external noise.
Main Methods:
- Numerical simulations of diffusively coupled nonlinear oscillators (Rössler and Lorenz models).
- Introduction of additional couplings at specific oscillator positions ((mN(c)+1)-th oscillators).
- Calculation of critical coupling strength (ε(c)) using synchronization error and conditional Lyapunov exponents.
- Analysis of synchronization error response to Gaussian white noise.
Main Results:
- Additional couplings significantly increase the maximum number of synchronized oscillators, overcoming size instability limitations.
- An exponential relationship was found between the number of synchronized oscillators and critical coupling strength (ε(c)) with a scaling exponent (γ).
- Synchronization error exhibits power-law decay with noise intensity, demonstrating noise-enhanced and noise-induced synchronization.
- Critical coupling strength (ε(c)) shows exponential decay with the number of additional couplings.
Conclusions:
- Strategic placement of additional couplings is an effective method to enhance chaos synchronization in oscillator networks.
- The findings provide insights into controlling and optimizing synchronization in complex dynamical systems.
- The study highlights the interplay between coupling, noise, and synchronization stability in nonlinear systems.
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