Conservation laws and symmetries in competitive systems

Lisa Uechi*, Tatsuya Akutsu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)210-222
Number of pages13
JournalProgress of Theoretical Physics Supplement
Issue number194
Publication statusPublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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