In this paper, a theorem on the uniqueness of limit cycle of the general Lienard equation is proved. Applying the theorem to the predator-prey model with undercrowding effect, it is proved that the predator-prey system has at most one limit cycle around the positive weak singular point.
Ping Guang ZHANG, Shen Qi ZHAO.
On the Uniqueness of Limit Cycle of the General Lienard Equation. Acta Mathematica Sinica, Chinese Series, 2004, 47(6): 1193-120 https://doi.org/10.12386/A2004sxxb0148