Journal
APPLIED MATHEMATICS LETTERS
Volume 62, Issue -, Pages 42-48Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2016.06.013
Keywords
Predator-prey model; Defense mechanism; Extinction domain; Limit cycle; Global dynamics
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Recently, Venturino and Petrovskii proposed a general predator prey model with group defense for prey species (Venturino and Petrovskii, 2013). The local dynamics had been studied and showed that the model might undergo Hopf bifurcation, and have an extinction domain. In this paper, we dedicate ourselves to the investigation of the global dynamics of the model by establishing the conditions of the nonexistence of periodic orbits, and the existence and uniqueness of limit cycles. (C) 2016 Elsevier Ltd. All rights reserved.
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