## 抄録

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.

本文言語 | English |
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ページ（範囲） | 210-222 |

ページ数 | 13 |

ジャーナル | Progress of Theoretical Physics Supplement |

号 | 194 |

出版ステータス | Published - 2012 |

外部発表 | はい |

## ASJC Scopus subject areas

- 物理学および天文学（その他）