### Abstract

We investigate a conservation law of a system of symmetric 2n-dimensional nonlinear differential equations. We use Lagrangian approach and Noether's theorem to analyze Lotka-Volterra type of competitive system. We observe that the coefficients of the 2n-dimensional nonlinear differential equations are strictly restricted when the system has a conserved quantity, and the relation between a conserved system and Lyapunov function is shown in terms of Noether's theorem. We find that a system of the 2n-dimensional first-order nonlinear differential equations in a symmetric form should appear in a binary-coupled form (BCF), and a BCF has a conserved quantity if parameters satisfy certain conditions. The conservation law manifests characteristic properties of a system of nonlinear differential equations and can be employed to check the accuracy of numerical solutions in the BCF.

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

Pages (from-to) | 210-222 |

Number of pages | 13 |

Journal | Progress of Theoretical Physics Supplement |

Issue number | 194 |

Publication status | Published - 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics Supplement*, (194), 210-222.

**Conservation laws and symmetries in competitive systems.** / Uechi, Lisa; Akutsu, Tatsuya.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics Supplement*, no. 194, pp. 210-222.

}

TY - JOUR

T1 - Conservation laws and symmetries in competitive systems

AU - Uechi, Lisa

AU - Akutsu, Tatsuya

PY - 2012

Y1 - 2012

N2 - We investigate a conservation law of a system of symmetric 2n-dimensional nonlinear differential equations. We use Lagrangian approach and Noether's theorem to analyze Lotka-Volterra type of competitive system. We observe that the coefficients of the 2n-dimensional nonlinear differential equations are strictly restricted when the system has a conserved quantity, and the relation between a conserved system and Lyapunov function is shown in terms of Noether's theorem. We find that a system of the 2n-dimensional first-order nonlinear differential equations in a symmetric form should appear in a binary-coupled form (BCF), and a BCF has a conserved quantity if parameters satisfy certain conditions. The conservation law manifests characteristic properties of a system of nonlinear differential equations and can be employed to check the accuracy of numerical solutions in the BCF.

AB - We investigate a conservation law of a system of symmetric 2n-dimensional nonlinear differential equations. We use Lagrangian approach and Noether's theorem to analyze Lotka-Volterra type of competitive system. We observe that the coefficients of the 2n-dimensional nonlinear differential equations are strictly restricted when the system has a conserved quantity, and the relation between a conserved system and Lyapunov function is shown in terms of Noether's theorem. We find that a system of the 2n-dimensional first-order nonlinear differential equations in a symmetric form should appear in a binary-coupled form (BCF), and a BCF has a conserved quantity if parameters satisfy certain conditions. The conservation law manifests characteristic properties of a system of nonlinear differential equations and can be employed to check the accuracy of numerical solutions in the BCF.

UR - http://www.scopus.com/inward/record.url?scp=84862523859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862523859&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84862523859

SP - 210

EP - 222

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 194

ER -