### 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 |
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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 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

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