Abstract
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.
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Gardini, L., Lupini, R. & Messia, M.G. Hopf bifurcation and transition to chaos in Lotka-Volterra equation. J. Math. Biology 27, 259–272 (1989). https://doi.org/10.1007/BF00275811
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DOI: https://doi.org/10.1007/BF00275811