Abstract
This paper is concerned with a prey-predator system with disease in the prey and two delays. Local stability of the positive equilibrium of the system and existence of local Hopf bifurcation are investigated by choosing different combinations of the two delays as bifurcation parameters. For further investigation, the direction and the stability of the Hopf bifurcation are determined by using the normal form method and center manifold theorem. Finally, some numerical simulations are given to support the theoretical analysis.
Highlights
The effect of disease in ecological system is an important issue from mathematical as well as ecological point of view
When the time delay is below the corresponding critical value, we get that the system is local stable
A local Hopf bifurcation occurs at the positive equilibrium
Summary
The effect of disease in ecological system is an important issue from mathematical as well as ecological point of view. The constant τ (τ ≥ 0) is the time delay due to susceptible prey which becomes the infected prey. There are some papers on the bifurcations of a prey-predator system with two or multiple delays [12,13,14,15,16]. It is reasonable to incorporate time delay due to the gestation of the predator into system (1) Based on this consideration, we consider the following system with two delays in this paper: dS (t) = rS (1 − S ) − αSI (t − τ1) − βSP , dt.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
