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Hopf bifurcations in 3D competitive system with mixing exponential and rational growth rates. (English) Zbl 07197743
Summary: This paper investigates a three-dimensional mixing competitive system with one exponential growth rate and two rational growth rates, whose nullclines are linearly determined. In total, 33 stable nullcline classes exist. Hopf bifurcations are studied in classes 26–31. We provide examples to prove the existence of at least two limit cycles in each of the classes 27–31.
37H20 Bifurcation theory for random and stochastic dynamical systems
37G10 Bifurcations of singular points in dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
Full Text: DOI
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