Hopf bifurcations in 3D competitive system with mixing exponential and rational growth rates

摘要

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.