Ratio-dependent predator-prey system with stage structure for prey
Xinyu Song - Department of Mathematics, Xinyang Teachers College, Henan 464000, China (email)
Abstract: A ratio-dependent predator-prey model with stage structure for the prey is proposed and analyzed, which improves the assumption that each individual prey has the same ability to be captured by predator. In this paper, mathematical analysis of the model equations with regard to boundedness of solutions, nature of equilibria, permanence are analyzed. We obtain conditions that determine the permanence of the populations. Furthermore, we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model. By the application of comparing argument and exploiting the monotonicity of one equation of the model, we obtain sufficient conditions for the global attractivity of positive equilibrium.
Keywords: Ratio-dependent, stage structure, permanence, stability.
Received: December 2002; Revised: February 2004; Published: May 2004.
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