Abstract
In this paper, a discrete hybrid three-species food chain system is proposed, where commercial harvesting on top predator is considered. Two time delays are introduced to represent gestation delay for prey and predator population, respectively. In absence of time delay, sufficient conditions associated with economic interest and step size are derived to show system undergoes flip bifurcation. In presence of double time delays, existence of Neimark–Sacker bifurcation and local stability switch are discussed due to variations of time delays. Furthermore, by utilizing new normal form of delayed discrete hybrid system and center manifold theorem, direction and stability of Neimark–Sacker bifurcation are studied. Numerical simulations are performed not only to validate theoretical analysis, but also exhibit cascades of period-doubling bifurcation, chaotic behavior and stable closed invariant curve.
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.
