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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
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