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This study explores multistability in chaotic maps, revealing how phase space segmentation and emergent channels drive deterministic chaotic diffusion. It examines both homogeneous and heterogeneous factors influencing this complex behavior.

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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.