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Cyclic synchronous patterns in coupled discontinuous maps.

Keli Yang1,2,3, Xingang Wang1,2, Shi-Xian Qu1,2

  • 1Institute of Theoretical & Computational Physics, Shaanxi Normal University, Xi'an 710062, China.

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Summary
This summary is machine-generated.

Researchers explored cyclic collective behaviors in coupled map lattices, revealing that competing synchronous clusters drive recurring patterns. Understanding these dynamics offers insights into biological systems and control strategies.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Cyclic collective behaviors are prevalent in biological and neuronal systems.
  • The underlying dynamical origins of these behaviors remain largely unexplained.
  • Understanding these patterns is crucial for fields like neuroscience and systems biology.

Purpose of the Study:

  • To investigate the dynamical origins of cyclic collective behaviors using models of coupled discontinuous map lattices.
  • To explore cluster synchronization as a mechanism for generating these behaviors.
  • To identify key factors influencing the emergence and control of cyclic patterns.

Main Methods:

  • Modeling coupled periodic piecewise-linear maps in lattices.
  • Analyzing synchronization behaviors in nonsynchronous regimes.
  • Investigating cluster dynamics, including expansion, shrinking, and switching.
  • Examining the role of basin distribution in pattern formation.

Main Results:

  • Identified cluster synchronization as a key mechanism for cyclic collective behaviors.
  • Observed competition between synchronous clusters leading to recurring patterns.
  • Revealed that basin distribution critically influences the dynamical mechanisms.
  • Demonstrated high sensitivity of cyclic patterns to initial conditions and parameters.

Conclusions:

  • Cluster synchronization in coupled discontinuous map lattices generates cyclic collective behaviors.
  • Basin distribution plays a crucial role in the dynamics of these patterns.
  • The sensitivity of these patterns allows for efficient control strategies.