Almost periodic solution of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and feedback controls
type: Item
instance of: scholarly article
title: Almost periodic solution of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and feedback controls
zbMATH Open document ID: 1406.92539
DOI: 10.1155/2014/252579
author: Kerong Zhang
author: Jianli Li
author: Aiwen Yu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider a modified Leslie-Gower predator-prey model with the Beddington-DeAngelis functional response and feedback controls as follows: \(\dot{x} \left(t\right) = x \left(t\right) \left(a_1 \left(t\right) - b \left(t\right) x \left(t\right) - c \left(t\right) y \left(t\right) / \left(\alpha \left(t\right) + \beta \left(t\right) x \left(t\right) + \gamma \left(t\right) y \left(t\right)\right) - e_1 \left(t\right) u \left(t\right)\right)\), \(\dot{u} \left(t\right) = - d_1 \left(t\right) u \left(t\right) + p_1 \left(t\right) x \left(t - \tau\right)\), \(\dot{y} \left(t\right) = y \left(t\right) \left(a_2 \left(t\right) - r \left(t\right) y \left(t\right) / \left(x \left(t\right) + k \left(t\right)\right) - e_2 \left(t\right) \nu \left(t\right)\right)\), and \(\dot{\nu}(t) = - d_2(t) \nu(t) + p_2(t) y(t - \tau)\). Sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7022008
zbMATH Keywords: Leslie-Gower predator-prey model
zbMATH Keywords: Beddington-DeAngelis functional response
zbMATH Keywords: feedback control
zbMATH Keywords: periodic solution
Wikidata QID: Q59036946
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/252579
OpenAlex ID: W2131154876
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description: scientific article; zbMATH DE number 7022008