Numerical Continuation and Bifurcation Analysis in a Harvested Predator-Prey Model with Time Delay using DDE-Biftool
Time delay has been incorporated in models to reflect certain physical or biological meaning. The theory of delay differential equations (DDEs), which has seen extensive growth in the last seventy years or so, can be used to examine the effects of time delay in the dynamical behaviour of systems being considered. Numerical tools to study DDEs have played a significant role not only in illustrating theoretical results but also in discovering interesting dynamics of the model. DDE-Biftool, which is a Matlab package for numerical continuation and numerical bifurcation analysis of DDEs, is one of the most utilized and popular numerical tools for DDEs. In this paper, we present a guide to using the latest version of DDE-Biftool targeted to researchers who are new to the study of time delay systems. A short discussion of an example application, which is a harvested predator-prey model with a single discrete time delay, will be presented first. We then implement this example model in DDE-Biftool, pointing out features where beginners need to be cautious. We end with a comparison of our theoretical and numerical results.
KeywordsDelay differential equations Numerical continuation Numerical bifurcation analysis Time delay systems
The author acknowledges the support of University of the Philippines Baguio, CIMPA, IMU-CDC, SEAMS, and Universiti Sains Malaysia for his participation to SEAMS School 2018 on Dynamical Systems and Bifurcation Analysis. The author also would like to thank the referees for their valuable reviews that improved the quality of this paper.
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