Mechanism of multistability in chaotic maps

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Complex Systems

Background:

• Multistability is a key phenomenon in chaotic systems, where multiple stable states coexist.
• Understanding the mechanisms of multistability is crucial for designing and controlling complex dynamical systems.
• Previous research has explored multistability in various contexts, but a unified framework for its emergence in chaotic maps is still developing.

Purpose of the Study:

• To investigate the fundamental mechanisms underlying homogeneous and heterogeneous multistability in chaotic maps.
• To explore the role of phase space segmentation and channel formation in deterministic chaotic diffusion.
• To analyze the influence of heterogeneous factors and phase transitions on multistability.

Main Methods:

• Analysis of a one-dimensional chain-climbing map to study homogeneous multistability.
• Introduction of heterogeneous factors to examine heterogeneous multistability.
• Investigation of phenomena like multistate intermittency and phase transitions.
• Case studies involving a memristive chaotic map and a hyperchaotic map.

Main Results:

• Phase space can segment into uniform mediums with consistent particle movement.
• Emergence of channels between mediums leads to deterministic chaotic diffusion at critical parameters.
• Multistate intermittency is closely linked to phase transitions and channel formation.
• Identified underlying factors contributing to multistability in memristive and hyperchaotic maps.

Conclusions:

• Homogeneous multistability arises from phase space segmentation and channel formation.
• Heterogeneous factors and phase transitions significantly influence multistability.
• The study provides a framework for understanding multistability in diverse chaotic maps.
• Findings offer insights into controlling and predicting chaotic system behavior.