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

Seong Lee; Inkyung Ahn

doi:10.3934/cpaa.2017022

Article Contents

2017, Volume 16, Issue 2: 427-442. Doi: 10.3934/cpaa.2017022

This issue Previous Article Center conditions for generalized polynomial kukles systems Next Article Existence and upper semicontinuity of (L², L^q) pullback attractors for a stochastic p-laplacian equation

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

Seong Lee and
Inkyung Ahn^,

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

Author Bio: imp57@korea.ac.kr
ahnik@korea.ac.kr
ahnik@korea.ac.kr

Received: January 31, 2016

Revised: October 31, 2016

Published: August 2017

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Abstract

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.

Keywords:

Diffusive predator-prey model,
Beddington-DeAngelis functional response,
time delay,
stage structure on prey,
locally/globally asymptotically stable.

Mathematics Subject Classification: 35K40, 35K57, 92D25.

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