TY - JOUR
T1 - Uniqueness of Limit Cycles in a Predator-Prey Model with Sigmoid Functional Response
AU - Zegeling , André
AU - Wang , Hailing
AU - Zhu , Guangzheng
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 790
EP - 802
PY - 2023
DA - 2023/12
SN - 5
DO - http://doi.org/10.12150/jnma.2023.790
UR - https://global-sci.org/intro/article_detail/jnma/22209.html
KW - Limit cycle, predator-prey system, Liénard equation, Sigmoid
functional response.
AB - <p style="text-align: justify;">In this paper, we prove that a predator-prey model with sigmoid
functional response and logistic growth for the prey has a unique stable limit
cycle, if the equilibrium point is locally unstable. This extends the results of
the 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 of
three versions of Zhang Zhifen’s uniqueness theorem for limit cycles in Liénard
systems to cover all possible limit cycle configurations. This technique can be
applied to a wide range of differential equations where at most one limit cycle
occurs.</p>