• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.327-344
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• 2005

The first part of the paper deals with a brief introduction of the plant-herbivore model system along with deterministic analysis of local stability and Hopf-bifurcations. The second part consists of stability analysis of the limit cycle arising from Hopf-bifurcation and uniqueness of limit cycle. The third part deals with the study of global stability of the model system under consideration.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.829-843
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• 2006

We propose a cubic differential system, which can be considered a generalization of the predator-prey models, studied by many authors recently (see [18, 20], for instance) The properties of the equilibrium points, the existences, nonexistence, the uniqueness conditions and the relative positions of the limit cycles are investigated. An example is used to show our theorems are easy to be used in applications.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.465-472
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• 2015

In this paper, we study the existence and the stability of equilibria of predator-prey models with Ivlev's functional response. We give a simple proof for the uniqueness of limit cycles of the predator-prey system. The existence and the stability at the origin and a boundary equilibrium point(including the positive equilibrium point) are also investigated.