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Synchronization of stochastic oscillations due to long-range diffusion.
A Efimov1, A Shabunin, A Provata
1Department of Physics, Saratov State University, Astrakhanskaya 83, Saratov 410026, Russia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
Summary
Adding diffusive mixing to the lattice Lotka-Volterra model synchronizes local oscillations. This leads to global limit cycle oscillations, demonstrating a nonequilibrium phase transition dependent on mixing rates.
Area of Science:
- Complex systems
- Statistical physics
- Chemical kinetics
Background:
- The cyclic lattice Lotka-Volterra (LLV) model exhibits fractal patterns and local oscillations on low-dimensional supports.
- Stochastic processes on catalytic supports are influenced by diffusive mixing.
- Understanding emergent phenomena in spatially extended systems is crucial.
Purpose of the Study:
- To investigate the impact of long-range diffusive mixing on stochastic processes.
- To analyze the emergence of global oscillations from local dynamics in the LLV model.
- To characterize the observed phenomenon as a nonequilibrium phase transition.
Main Methods:
- Utilizing the cyclic lattice Lotka-Volterra (LLV) model as a working example.
- Introducing a weak, long-range diffusive mixing process to the LLV model.
- Analyzing the system's behavior by varying the mixing-to-reaction rate (p).
Main Results:
- Local oscillations within the LLV model synchronize upon the addition of diffusive mixing.
- Global oscillations of a limit cycle type emerge above a critical mixing rate (p_c).
- The critical point (p_c) is dependent on the model's kinetic parameters.
Conclusions:
- Diffusive mixing can induce phase synchronization and global oscillations in spatially extended systems.
- The emergence of global oscillations represents a nonequilibrium phase transition.
- The study highlights the interplay between reaction dynamics and diffusive transport in complex systems.
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