### 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 |

### Fingerprint

### 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

*Discrete and Continuous Dynamical Systems - Series S*, (SUPPL.), 685-694.

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

Research output: Contribution to journal › Article

*Discrete and Continuous Dynamical Systems - Series S*, no. SUPPL., pp. 685-694.

}

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 -