Intermingled basins and on-off intermittency in a multistate system

Area of Science:

• Dynamical Systems and Chaos Theory
• Nonlinear Dynamics
• Statistical Physics

Background:

• Dynamical systems can exhibit complex behaviors within invariant subspaces.
• Intermingled basins of attraction are observed between coexisting chaotic states.
• Parameter variations can lead to transitions in system dynamics.

Purpose of the Study:

• To investigate the dynamics of a system with infinite low-dimensional symmetric invariant subspaces, each hosting a chaotic state.
• To analyze the transition from intermingled basin dynamics to multistate on-off intermittency.
• To examine the statistical behavior and physical transport properties associated with these different dynamic states.

Main Methods:

• Analysis of dynamical systems with invariant subspaces.
• Characterization of chaotic states and basin structures.
• Calculation of Lyapunov exponents to identify dynamic transitions.
• Investigation of statistical properties and transport phenomena.

Main Results:

• The system exhibits infinite symmetric invariant subspaces, each with a chaotic state.
• Stable chaotic states lead to intermingled basins.
• A transition from intermingled basins to multistate on-off intermittency occurs as the transverse Lyapunov exponent becomes positive.
• Detailed analysis of statistical behavior and physical transport for different dynamic states.

Conclusions:

• The study elucidates the complex interplay between invariant subspaces, chaotic dynamics, and parameter-driven transitions.
• The findings provide insights into the mechanisms governing intermingled basins and on-off intermittency.
• Understanding these dynamics is crucial for predicting statistical behavior and transport properties in complex systems.