Abstract
In this paper we consider a delayed population model with delay-dependent parameters. Its dynamics are studied in terms of stability and Hopf bifurcations. We prove analytically that the positive equilibrium switches from being stable to unstable and then back to stable as the delay τ increases, and Hopf bifurcations occur finite times between the two critical values of stability changes. Moreover, the critical values for stability switches and Hopf bifurcations can be analytically determined. Using the perturbation approach and Floquet technique, we also obtain an approximation to the bifurcating periodic solution and derive the formulas for determining the direction and stability of the Hopf bifurcations. Finally, we illustrate our results with some numerical examples.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.