Stability and Hopf bifurcation periodic orbits in delay coupled Lotka-Volterra ring system. (English) Zbl 1426.37042
Summary: In this paper, we consider a class of delay coupled Lotka-Volterra ring systems. Based on the symmetric bifurcation theory of delay differential equations and representation theory of standard dihedral groups, properties of phase locked periodic solutions are given. Moreover, the direction and the stability of the Hopf bifurcation periodic orbits are obtained by using normal form and center manifold theory. Finally, the research results are verified by numerical simulation.
MSC:
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 37C10 | Dynamics induced by flows and semiflows |
| 34K20 | Stability theory of functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
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