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On the first Liapunov coefficient formula of 3D Lotka-Volterra equations with applications to multiplicity of limit cycles.
- Source :
-
Journal of Differential Equations . May2021, Vol. 284, p183-218. 36p. - Publication Year :
- 2021
-
Abstract
- This paper provides the first Liapunov coefficient formula of 3D Lotka-Volterra equations. This formula gives applications to stability of positive equilibrium and to detecting sub/super criticality of Hopf bifurcation. For 3D competitive Lotka-Volterra equations, combining this formula with the Poincaré-Bendixson theorem, we obtain criteria on multiplicity of limit cycles among Zeeman's classes 27-31, and present a series of examples to admit at least two limit cycles, which are rigorously proved by the first Liapunov coefficient formula, rather than by symbolic computation using Maple. A new Hopf bifurcation that all 2 × 2 principal minors of the community matrix are positive is found, and numerical simulation reveals its global limit cycle bifurcations are plenty. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 284
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 149471263
- Full Text :
- https://doi.org/10.1016/j.jde.2021.02.059