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Numerical continuation and bifurcation analysis in a harvested predator-prey model with time delay using DDE-biftool. (English) Zbl 1447.34003
Mohd, Mohd Hafiz (ed.) et al., Dynamical systems, bifurcation analysis and applications. Collected papers of the SEAMS school 2018 on dynamical systems and bifurcation analysis, DySBA, Penang, Malaysia, August 6–13, 2018. Singapore: Springer. Springer Proc. Math. Stat. 295, 225-241 (2019).
Summary: Time delay has been incorporated in models to reflect certain physical or biological meaning. The theory of delay differential equations (DDEs) 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.
For the entire collection see [Zbl 1443.37004].
MSC:
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34K18 Bifurcation theory of functional-differential equations
37M20 Computational methods for bifurcation problems in dynamical systems
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