eng
International Academy of Ecology and Environmental Sciences
Computational Ecology and Software
2220-721X
2020-3-1
10
1
15
43
2
article
Local dynamical properties and supercritical N-S bifurcation of a
discrete-time host-parasitoid model with Allee effect
A. Q. Khan
1
2
M. Askari
1
2
H. S. Alayachi
1
2
M. S. M. Noorani
1
2
Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor,
Malaysia
We explore thelocal dynamical properties and supercritical N-S bifurcation of the following Beddington model with Allee effect in R2+:
xt+1=xt exp(r(1-xt)-yt), yt+1=m xt (1-exp(-yt)) yt/(B+yt),
where xt (respectively yt) denotes densities of host (respectively parasitoid) at time t, r and m respectively denotes number of eggs laid by host and parasitoid which survive through larvae, pupae, and adult stages, and B is constant. More specifically, we explored that model has three equilibria namely the trivial, boundary and positive equilibrium point. We studied the local dynamics along with topological classification about equilibria of the under consideration model. We also explored the existence of bifurcation about equilibria of the model. It is proved about boundary equilibrium point parasitoidgoes to extinction whilehost population undergoes a flip bifurcation to chaos by taking r as bifurcation parameter. It is explored that aboutpositive equilibrium point, model undergoes N-S bifurcation and in meantime invariant closed curve appears. In the perspective of the biology, these curves correspond to periodic or quasi-periodic oscillations between host and parasitoid populations. Finally theoretical results are verified numerically.
http://www.iaees.org/publications/journals/ces/articles/2020-10(1)/discrete-time-host-parasitoid-model-with-Allee-effect.pdf
Beddington model
stability and bifurcation
Allee effect
numerical simulation