TY - JOUR
T1 - Dynamics of a Predator-Prey Reaction-Diffusion System with Non-Monotonic Functional Response Function
AU - Wang , Huan
AU - Zhang , Cunhua
JO - Annals of Applied Mathematics
VL - 2
SP - 199
EP - 220
PY - 2022
DA - 2022/06
SN - 34
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20573.html
KW - reaction-diffusion system, predator-prey system, asymptotic
stability, Hopf bifurcation.
AB - <p style="text-align: justify;">In this article, a two-species predator-prey reaction-diffusion system with
Holling type-IV functional response and subject to the homogeneous Neumann
boundary condition is regarded. In the absence of the spatial diffusion, the
local asymptotic stability, the instability and the existence of Hopf bifurcation
of the positive equilibria of the corresponding local system are analyzed in
detail by means of the basic theory for dynamical systems. As well, the effect
of the spatial diffusion on the stability of the positive equilibria is considered
by using the linearized method and analyzing in detail the distribution of roots
in the complex plane of the associated eigenvalue problem. In order to verify
the obtained theoretical predictions, some examples and numerical simulations
are also included by applying the numerical methods to solve the ordinary and
partial differential equations.</p>