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Related Experiment Videos

Delayed coupling of logistic maps.

C Masoller1, H L Cavalcante, J R Leite

  • 1Instituto de Física, Facultad de Ciencias, Universidad de la República, Igua 4225, Montevideo 11400, Uruguay.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

We investigated logistic map synchronization with one-way coupling and delays. Perfect synchronization occurs when the slave has no delay, while generalized synchronization is observed with slave delays.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Complex systems

Background:

  • Coupled chaotic systems exhibit complex behaviors.
  • Synchronization phenomena are crucial in various scientific fields.
  • Logistic maps are fundamental models for studying chaos.

Purpose of the Study:

  • To analyze synchronization in one-way coupled delayed logistic maps.
  • To investigate the impact of delays on synchronization regimes.
  • To differentiate true synchronization from noise-induced correlations.

Main Methods:

  • One-way coupling configuration of master and slave logistic maps.
  • Introduction of delays n(1) and n(2) in the coupling and slave systems.
  • Development of a similarity function to quantify synchronization.
  • Utilizing a noisy master source to distinguish synchronization from noise.

Main Results:

  • Perfect synchronization achieved when slave delay n(2)=0 and coupling is sufficiently strong.
  • Generalized synchronization observed when slave delay n(2)≠0, characterized by y(i+n(1))=x(i) but different maps.
  • Similarity function effectively indicates the degree of synchronization.
  • Distinction between synchronization and noise-induced correlations demonstrated.

Conclusions:

  • Delay in the slave system fundamentally alters synchronization dynamics.
  • Generalized synchronization represents a distinct state in coupled chaotic systems.
  • The developed methods reliably characterize synchronization in the presence of noise.

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