Abstract
In this paper, a delayed eco-epidemiological model with disease in prey, anti-predator factor for the prey and stage structure for the predator is proposed. The conditions for the stability and coexistence of the populations have been derived. Positivity and boundedness of all solutions with positive initial conditions has been proved. Sufficient conditions for the occurrence of several Hopf and Bogdanov–Takens bifurcations about the endemic steady state are derived. By taking the delay as the bifurcation parameter, it is shown that Hopf and Bogdanov–Takens bifurcations occur at positive steady state for some critical values of the delay. The normal form of the Bogdanov–Takens singularity is obtained by performing a center manifold reduction and by using the normal form theory of FDEs. Some numerical simulations of solutions in different parametric regions illustrating Hopf and homoclinic bifutcations are given to support the analytical results.
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.
