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Asymptotic behavior of a ratio-dependent predator-prey system with disease in the prey

Pages: 11 - 19, Issue special, November 2013

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Inkyung Ahn - Department of Information and Mathematics, Korea University, Jochiwon 339-700, South Korea (email)
Wonlyul Ko - Department of Information and Mathematics, Korea University, Jochiwon 339-700, South Korea (email)
Kimun Ryu - Department of Mathematics Education, Cheongju University, Cheongju, Chungbuk 360-764, South Korea (email)

Abstract: In this paper, we consider a ratio-dependent predator-prey model with disease in the prey under Neumann boundary condition. we construct a global attractor region for all time-dependent non-negative solutions of the system and investigate the asymptotic behavior of positive constant solution. Furthermore, we also study the asymptotic behavior of the non-negative equilibria.

Keywords:  Ratio-dependent, predator-prey, disease-free, asymptotic stability.
Mathematics Subject Classification:  35K55, 35J60.

Received: September 2012;      Revised: January 2013;      Published: November 2013.

 References