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 language | English |
|---|---|
| Pages (from-to) | 685-694 |
| Number of pages | 10 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Issue number | SUPPL. |
| Publication status | Published - 2013 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Control of attractors in nonlinear dynamical systems using external noise
T2 - Effects of noise on synchronization phenomena
AU - Shiino, Masatoshi
AU - Okumura, Keiji
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Control of attractors
KW - Exactly solvable mean-field models
KW - Noise-induced chaos and limit cycles
KW - Noise-induced synchronization
KW - Nonequilibrium phase transitions
KW - Nonlinear Fokker-Planck equations
UR - http://www.scopus.com/inward/record.url?scp=84901403235&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84901403235&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84901403235
SP - 685
EP - 694
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
SN - 1937-1632
IS - SUPPL.
ER -