Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 26, Issue 7, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127416501170
Keywords
Predator-prey model; Allee effect; time delay; triple-zero bifurcation; stability
Funding
- National Natural Science Foundation of China [11201294, 11571257]
- Innovation Program of Shanghai Municipal Education Commission [14YZ114]
- Natural Science and Engineering Research Council of Canada [R2686A02]
Ask authors/readers for more resources
In this paper, a Leslie-type predator-prey model with ratio-dependent functional response and Allee effect on prey is considered. We first study the existence of the multiple positive equilibria and their stability. Then we investigate the effect of delay on the distribution of the roots of characteristic equation and obtain the conditions for the occurrence of simple-zero, double-zero and triple-zero singularities. The formulations for calculating the normal form of the triple-zero bifurcation of the delay differential equations are derived. We show that, under certain conditions on the parameters, the system exhibits homoclinic orbit, heteroclinic orbit and periodic orbit.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available