# American Institute of Mathematical Sciences

March  2017, 16(2): 427-442. doi: 10.3934/cpaa.2017022

## Diffusive predator-prey models with stage structure on prey and beddington-deangelis functional responses

 Department of Mathematics, Korea University, 2511, Sejong-Ro, Sejong, 30019, Korea

ahnik@korea.ac.kr

Received  February 2016 Revised  November 2016 Published  January 2017

In this paper, we examine a diffusive predator-prey model with Beddington-DeAngelis functional response and stage structure on prey under homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of immature prey to their maturity. We investigate the dynamics of their permanence and the extinction of the predator, and provide sufficient conditions for the global attractiveness and the locally asymptotical stability of the semi-trivial and coexistence equilibria.

Citation: Seong Lee, Inkyung Ahn. Diffusive predator-prey models with stage structure on prey and beddington-deangelis functional responses. Communications on Pure & Applied Analysis, 2017, 16 (2) : 427-442. doi: 10.3934/cpaa.2017022
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