Three limit cycles for a three-dimensional Lotka-Volterra competitive system with a heteroclinic cycle
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Publication:597221
DOI10.1016/S0898-1221(03)90027-7zbMath1053.34030MaRDI QIDQ597221
Publication date: 6 August 2004
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
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Cites Work
- Unnamed Item
- Unnamed Item
- Applications of centre manifold theory
- Multiple limit cycles for three dimensional Lotka-Volterra equations
- Limit cycles for the competitive three dimensional Lotka-Volterra system
- Two limit cycles in three-dimensional Lotka-Volterra systems
- Systems of differential equations which are competitive or cooperative: III. Competing species
- Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems
- Three-Dimensional Competitive Lotka--Volterra Systems with no Periodic Orbits
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