Uniqueness of Limit Cycles in a Predator-Prey Model with Sigmoid Functional Response (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we prove that a predator-prey model with sigmoidfunctional response and logistic growth for the prey has a unique stable limitcycle, if the equilibrium point is locally unstable. This extends the results ofthe literature where it was proved that the equilibrium point is globally asymptotically stable, if it is locally stable. For the proof, we use a combination ofthree versions of Zhang Zhifen’s uniqueness theorem for limit cycles in Liénardsystems to cover all possible limit cycle configurations. This technique can beapplied to a wide range of differential equations where at most one limit cycleoccurs.
Keywords: Limit cycle; predator-prey system; Liénard equation; Sigmoid functional response.