Hopf bifurcation and transition to chaos in Lotka-Volterra equation. (English) Zbl 0715.92020
Summary: It is shown that in a suitable class of Lotka-Volterra systems it is possible to characterize the centre-critical case of the Hopf bifurcation of the multipopulation equilibrium. Moreover, for three populations, it is shown that, in the non-critical case, Hopf bifurcation is supercritical. Numerical evidence of transition to chaotic dynamics, via period-doubling cascades, from the limit cycle is reported.
MSC:
| 92D25 | Population dynamics (general) |
| 37G99 | Local and nonlocal bifurcation theory for dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
Volterra equation; strange attractor; Lotka-Volterra systems; centre- critical case; Hopf bifurcation; multipopulation equilibrium; three populations; non-critical case; supercritical; transition to chaotic dynamics; period-doubling cascades; limit cycleReferences:
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