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Transient spatiotemporal chaos is extensive in three reaction-diffusion networks
Dan Stahlke1, Renate Wackerbauer
1Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920, USA. dstahlke@gmail.com
Summary
Extensive spatiotemporal chaos exhibits similar subsystems with weak interactions. Transient behavior in reaction-diffusion networks shows linear growth in dimension and lifetime with system size.
Area of Science:
- Nonlinear dynamics
- Complex systems science
- Chemical kinetics
Background:
- Extensive spatiotemporal chaos involves statistically similar subsystems with weak interactions.
- Understanding transient dynamics is crucial for characterizing complex systems.
Purpose of the Study:
- To systematically study transient spatiotemporal chaos in reaction-diffusion networks.
- To investigate how system size affects chaotic properties and transient behavior.
Main Methods:
- Analysis of three reaction-diffusion networks under various boundary conditions.
- Calculation of Lyapunov dimension, sum of positive Lyapunov exponents, and transient lifetime.
- Characterization of unstable and stable manifolds of chaotic saddles.
Main Results:
- Extensive system behavior was observed across all tested networks.
- Lyapunov dimension, sum of positive Lyapunov exponents, and logarithm of transient lifetime scale linearly with system size.
- The unstable manifold dimension approximates the saddle dimension, and the stable manifold is nearly space-filling.
Conclusions:
- Transient spatiotemporal chaos in these systems demonstrates extensive properties.
- System size is a key factor influencing the dimensionality and lifetime of chaotic transients.
- The geometric properties of chaotic saddles provide insights into the system's dynamics.
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