Abstract. 

An analytical and numerical analysis of the transition to chaos was carried out in the model proposed by A.D. Bazykin for the dynamics of the number of interacting populations of a predator and two prey. The conditions for the creation of a periodic solution as a result of the Andronov-Hopf bifurcation are found. It is shown numerically that the transition to chaos in the system of differential equations describing the dynamics of interacting populations is carried out in full accordance with the Feigenbaum-Sharkovsky-Magnitskii universal bifurcation theory (FShM) through subharmonic and homoclinic bifurcation cascades of stable limit cycles.

Keywords: population dynamics, predator-prey model, bifurcation cascades, FShM theory, attractors, chaos.

PP. 71-74.

DOI: 10.14357/20790279200208

 

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