Mathematical Biology Seminar
Feb 26, 12:00pm-1:00pm in MSB 318
Speaker: Dr. Chunhua Shan (U Toledo)
Title: Global Hopf bifurcation and connected components in a simple delayed predator-prey model
Abstract: In this talk we will consider the local and global Hopf bifurcations in a delayed predator-prey model. We will show that there exists a sequence of local Hopf bifurcations as parameter delay $\tau$ varies and that the connected components of the global Hopf bifurcation are nested under certain conditions. Furthermore, the limit cycle of the classical predator-prey model is an element of a connected component of the global Hopf bifurcation. The joint impact of the delay and environmental carrying capacity is revealed. It turns out that the predator and prey may coexist in an oscillatory pattern with lower environmental carrying capacity for $\tau>0$ compared to that for $\tau=0$ which is counterintuitive.
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