TY - JOUR
T1 - Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 376
EP - 395
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.020916.250217a
UR - https://global-sci.org/intro/article_detail/eajam/10755.html
KW - Predator-prey system, Holling type IV functional response, periodic solution, bifurcation, Lyapunov function.
AB - <p style="text-align: justify;">We investigate the stability and periodic orbits of a predator-prey model with
harvesting. The model has a biologically-meaningful interior, an attractor undergoing
damped oscillations, and can become destabilised to produce periodic orbits via a Hopf
bifurcation. Some sufficient conditions for the existence of the Hopf bifurcation are
established, and a stability analysis for the periodic solutions using a Lyapunov function
is presented. Finally, some computer simulations illustrate our theoretical results.</p>