### Abstract

Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation is studied numerically and theoretically, and the statistical, feature is analyzed precisely in reference to the onset mechanism of the turbulence. First, the bifurcation diagram is demonstrated in detail, and a variety of attractors are discussed. It is emphasized that the diversity of the attractor enhances when the system size increases. Next, the transition from a regular attractor to a turbulent one is characterized by a correlation function, as well as by the Lyapunov exponent, where one can observe the scaling laws clearly for the correlation length and the maximum Lyapunov exponent.

Original language | English |
---|---|

Pages (from-to) | 267-271 |

Number of pages | 5 |

Journal | Journal of the Korean Physical Society |

Volume | 50 |

Issue number | 1 I |

Publication status | Published - 2007 Jan |

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### Keywords

- Correlation length
- Heteroclinicity
- Lotka-Volterra equation
- Maximum Lyapunov exponent
- May-Leonard model
- Scaling relation
- Spatio-temporal chaos
- Turbulence

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Korean Physical Society*,

*50*(1 I), 267-271.

**Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation.** / Orihashi, Kenji; Aizawa, Yoji.

Research output: Contribution to journal › Article

*Journal of the Korean Physical Society*, vol. 50, no. 1 I, pp. 267-271.

}

TY - JOUR

T1 - Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation

AU - Orihashi, Kenji

AU - Aizawa, Yoji

PY - 2007/1

Y1 - 2007/1

N2 - Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation is studied numerically and theoretically, and the statistical, feature is analyzed precisely in reference to the onset mechanism of the turbulence. First, the bifurcation diagram is demonstrated in detail, and a variety of attractors are discussed. It is emphasized that the diversity of the attractor enhances when the system size increases. Next, the transition from a regular attractor to a turbulent one is characterized by a correlation function, as well as by the Lyapunov exponent, where one can observe the scaling laws clearly for the correlation length and the maximum Lyapunov exponent.

AB - Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation is studied numerically and theoretically, and the statistical, feature is analyzed precisely in reference to the onset mechanism of the turbulence. First, the bifurcation diagram is demonstrated in detail, and a variety of attractors are discussed. It is emphasized that the diversity of the attractor enhances when the system size increases. Next, the transition from a regular attractor to a turbulent one is characterized by a correlation function, as well as by the Lyapunov exponent, where one can observe the scaling laws clearly for the correlation length and the maximum Lyapunov exponent.

KW - Correlation length

KW - Heteroclinicity

KW - Lotka-Volterra equation

KW - Maximum Lyapunov exponent

KW - May-Leonard model

KW - Scaling relation

KW - Spatio-temporal chaos

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=33846675882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846675882&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33846675882

VL - 50

SP - 267

EP - 271

JO - Journal of the Korean Physical Society

JF - Journal of the Korean Physical Society

SN - 0374-4884

IS - 1 I

ER -