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Global Qualitative Analysis for a Ratio-Dependent Predator–Prey Model with Delay

✍ Scribed by Sanyi Tang; Lansun Chen

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
147 KB
Volume
266
Category
Article
ISSN
0022-247X

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✦ Synopsis

A ratio-dependent predator-prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given.  2002 Elsevier Science (USA)

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