Control of attractors in nonlinear dynamical systems using external noise: Effects of noise on synchronization phenomena

Masatoshi Shiino, Keiji Okumura

Research output: Contribution to journalArticle

Abstract

Synchronization phenomena occurring as a result of cooperative ones are ubiquitous in nonequilibrium physical and biological systems and also are considered to be of vital importance in information processing in the brain. Those systems, in general, are subjected to various kinds of noise. While in the case of equilibrium thermodynamic systems external Langevin noise is well-known to play the role of heat bath, few systematic studies have been conducted to explore effects of noise on nonlinear dynamical systems with many degrees of freedom exhibiting limit cycle oscillations and chaotic motions, due to their complexity. Considering simple nonlinear dynamical models that all-flow rigorous analyses based on use of nonlinear Fokker-Planck equations, we conduct systematic studies to observe effects of noise on oscillatory behavior with changes in several kinds of parameters characterising mean-field coupled oscillator ensembles and excitable element ones. Phase diagrams representing the dependence of the largest and the second largest Lyapunov exponents on the noise strength are studied to show the appearance and disappearance of synchronization of limit cycle oscillations.

Original languageEnglish
Pages (from-to)685-694
Number of pages10
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue numberSUPPL.
Publication statusPublished - 2013
Externally publishedYes

Fingerprint

Nonlinear dynamical systems
Nonlinear Dynamical Systems
Limit Cycle
Attractor
Synchronization
Nonlinear Fokker-Planck Equations
Oscillation
Fokker Planck equation
Largest Lyapunov Exponent
Heat Bath
Thermodynamic Equilibrium
Chaotic Motion
Coupled Oscillators
Biological systems
Dynamical Model
Information Processing
Biological Systems
Mean Field
Phase Diagram
Non-equilibrium

Keywords

  • Control of attractors
  • Exactly solvable mean-field models
  • Noise-induced chaos and limit cycles
  • Noise-induced synchronization
  • Nonequilibrium phase transitions
  • Nonlinear Fokker-Planck equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Control of attractors in nonlinear dynamical systems using external noise : Effects of noise on synchronization phenomena. / Shiino, Masatoshi; Okumura, Keiji.

In: Discrete and Continuous Dynamical Systems - Series S, No. SUPPL., 2013, p. 685-694.

Research output: Contribution to journalArticle

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