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Nonchaotic stagnant motion in a marginal quasiperiodic gradient system
1Department of Applied Physics, Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan. t.mitsui@aoni.waseda.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
This study introduces a novel dynamical system with quasiperiodic gradients, revealing nonchaotic intermittent motion. Its unique properties, including an inverse-square law for residence times, differ significantly from standard intermittent chaos.
Area of Science:
- Dynamical Systems
- Nonlinear Dynamics
- Mathematical Physics
Background:
- Nonuniform oscillators and intermittent chaos are known phenomena in dynamical systems.
- Understanding intermittent behavior is crucial for modeling complex systems.
- Quasiperiodic forcing can lead to unique dynamical behaviors.
Purpose of the Study:
- To introduce and analyze a one-dimensional dynamical system with a marginal quasiperiodic gradient.
- To investigate the nonchaotic stagnant motion and its relation to intermittent chaos.
- To theoretically derive the asymptotic long-time behavior and compare it with existing models.
Main Methods:
- Mathematical modeling of a one-dimensional dynamical system.
- Analysis of the density function of residence times near stagnation points.
- Theoretical derivation of asymptotic long-time behavior.
- Comparison with Pomeau-Manneville intermittency.
Main Results:
- The system exhibits nonchaotic stagnant motion, resembling intermittent chaos.
- Residence time density follows an inverse-square law, similar to type-I intermittency.
- The alternation between stagnant and moving phases is quasiperiodic, not random.
- For a golden ratio gradient, residence time renewal aligns with the Fibonacci sequence.
- Asymptotic long-time behavior is theoretically derived as a nested logarithm.
- Significant differences in relaxation properties are observed compared to Pomeau-Manneville intermittency.
Conclusions:
- The presented dynamical system offers a novel model for quasiperiodic intermittency.
- The system's behavior, particularly the quasiperiodic alternation and Fibonacci sequence correlation, distinguishes it from random intermittency.
- The theoretical derivation provides insights into the long-time dynamics and relaxation properties.
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