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Two-state on-off intermittency caused by unstable dimension variability in periodically forced drift waves
P P Galuzio1, S R Lopes, R L Viana
1Departamento de Física, Universidade Federal do Paraná, Curitiba, Paraná, Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
High-dimensional dynamical systems exhibiting two-state on-off intermittency show dynamics oscillating between attractors. This behavior stems from unstable dimension variability, a breakdown of attractor hyperbolicity, as shown in forced drift waves.
Area of Science:
- Dynamical Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Complex dynamical systems can exhibit multiple attractors with distinct energy levels.
- Two-state on-off intermittency is a phenomenon where dynamics randomly switch between these attractors.
Purpose of the Study:
- To elucidate the underlying dynamical mechanism of two-state on-off intermittency.
- To investigate the role of unstable dimension variability in this phenomenon.
- To analyze the parametric evolution of unstable dimension variability.
Main Methods:
- Analysis of high-dimensional dynamical systems.
- Characterization of attractor hyperbolicity breakdown.
- Statistical analysis of finite-time Lyapunov exponents.
- Modeling with periodically forced and damped drift waves.
Main Results:
- Unstable dimension variability is identified as the core mechanism behind two-state on-off intermittency.
- The parametric evolution of unstable dimension variability is quantitatively characterized.
- A spatiotemporal model (drift waves) demonstrates this behavior, featuring a chaotic attractor formed by an interior crisis.
Conclusions:
- Unstable dimension variability is crucial for understanding on-off intermittency in complex systems.
- Finite-time Lyapunov exponents provide a robust method for quantifying this variability.
- The findings offer insights into chaotic dynamics in spatiotemporal systems.
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