Limit Cycles in a Class of Quartic Kolmogorov Model with Three Positive Equilibrium Points

作者：Du, Chaoxiong^*; Liu, Yirong; Zhang, Qi

来源：International Journal of Bifurcation and Chaos, 2015, 25(6): 1550080.

DOI：10.1142/S0218127415500807

• Kolmogorov model
• limit cycles
• Poincare succession function
• center problem

Limit cycle bifurcation problem of Kolmogorov model is interesting and significant both in theory and applications. In this paper, we will focus on investigating limit cycles for a class of quartic Kolmogorov model with three positive equilibrium points. Perturbed model can bifurcate three small limit cycles near (1, 2) or ( 2, 1) under a certain condition and can bifurcate one limit cycle near (1, 1). In addition, we have given some examples of simultaneous Hopf bifurcation and the structure of limit cycles bifurcated from three positive equilibrium points. The limit cycle bifurcation problem for Kolmogorov model with several positive equilibrium points are less seen in published references. Our result is good and interesting.

• 出版日期2015-6
• 单位邵阳学院