TY - JOUR
T1 - Complex Dynamical Behaviors of a Leslie-Gower Predator-Prey Model with Herd Behavior
AU - Chen , Xiaohui
AU - Yang , Wensheng
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1064
EP - 1082
PY - 2024
DA - 2024/12
SN - 6
DO - http://doi.org/10.12150/jnma.2024.1064
UR - https://global-sci.org/intro/article_detail/jnma/23672.html
KW - Leslie-Gower predator-prey model, herd behavior, stability, Hopf
bifurcation, limit cycle.
AB - <p style="text-align: justify;">In this paper, we consider a Leslie-Gower predator-prey model
with a square root functional response while prey forms a herd as a form of
group defense. We show that the solution of the system is non-negative and
bounded. By applying the blow-up technique, it can be deduced that the
origin displays instability. Moreover, employing the proof-by-contradiction
approach, we demonstrate that the unique equilibrium point can be globally
asymptotically stable under certain conditions. The sufficient conditions for
the occurrence, stability, and direction of Hopf bifurcation are obtained. We
further explore the conditions for the existence and uniqueness of the limit
cycle. Theoretical results are validated through numerical simulations. Thus,
our findings reveal that herd behavior has an important impact on the Leslie-Gower prey-predator system.</p>