Title:
Relaxation Oscillations in a Class of Predator-Prey Systems
Relaxation Oscillations in a Class of Predator-Prey Systems
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Author(s)
Liu, Weishi
Xiao, Dongmei
Yi, Yingfei
Xiao, Dongmei
Yi, Yingfei
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Abstract
We consider a class of three dimensional, singularly perturbed predator-prey systems having two predators competing exploitatively for the same prey in a constant environment. By using dynamical systems techniques and the geometric singular perturbation theory, we give precise conditions which guarantee the existence of stable relaxation oscillations for systems within the class. Such result shows the coexistence of the predators and the prey with quite diversified time response which typically happens when the
prey population grows much faster than those of predators. As an application, a well-known model will be discussed in detail by showing the existence of stable relaxation oscillations for a wide range of parameters values of the model.
Sponsor
The first author is partially supported by NSF Grant DMS-0071931. The second author is partially supported by NSF-China Grant 10071027. The third author is partially supported by NSF Grant DMS-9803581.
Date Issued
2001
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Pre-print