On the Stability Analysis of a Reaction-Diffusion Predator-Prey Model Incorporating Prey Refuge

被引：0

作者：

Lazaar O. ^{[1
]}

Serhani M. ^{[2
]}

Alla A. ^{[3
]}

Raissi N. ^{[3
]}

机构：

[1] TSI Team, MACS Laboratory, Faculty of Sciences, Moulay Ismail University of Meknès, Meknes, Zitoune

[2] TSI Team, MACS Laboratory, Faculty of SJES, Moulay Ismail University of Meknès, B.P. 3102, Meknes, Toulal

[3] ANLIMAD Team, LAMA Laboratory, Faculty of Sciences, Mohammed V University in Rabat, Rabat

来源：

International Journal of Applied and Computational Mathematics | 2022年 / 8卷 / 4期

关键词：

Global existence; Global stability analysis; Lotka–Volterra model; Lyapunov function; Reaction-diffusion equations;

D O I：

10.1007/s40819-022-01415-0

中图分类号：

学科分类号：

摘要：

This paper aims to investigate the stability behavior of a spatio-temporal prey-predator model. The goal is to study, in the framework of a two-dimensional space reaction-diffusion Lotka–Volterra predator-prey model, extended by Holling type III functional responses and incorporating prey refuge, the impact of refuge on the dynamic behavior of both prey and predator. We provide hence, the global existence of a strong solution for the model with positive initial values and its boundedness. Moreover, we investigate the local and global Lyapunov stability for this reaction-diffusion system, using the spectral analysis and LaSalle invariance principle in a Banach space. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

引用

共 50 条

[1] Existence of spatiotemporal patterns in the reaction-diffusion predator-prey model incorporating prey refuge
Guin, Lakshmi Narayan
Mondal, Benukar
Chakravarty, Santabrata
[J]. INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2016, 9 (06)
[2] Delay-driven pattern formation in a reaction-diffusion predator-prey model incorporating a prey refuge
Lian, Xinze
Wang, Hailing
Wang, Weiming
[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2013,
[3] Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge
Wang, Lingshu
Feng, Guanghui
[J]. JOURNAL OF APPLIED MATHEMATICS, 2014,
[4] Stability analysis: The effect of prey refuge in predator-prey model
Ma, Zhihui
Wang, Shufan
[J]. ECOLOGICAL MODELLING, 2012, 247 : 95 - 97
[5] Analysis of a predator-prey model with herd behavior and disease in prey incorporating prey refuge
Saha, Sangeeta
Samanta, G. P.
[J]. INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2019, 12 (01)
[6] Qualitative Analysis for a Reaction-Diffusion Predator-Prey Model with Disease in the Prey Species
Qiao, Meihong
Liu, Anping
Forys, Urszula
[J]. JOURNAL OF APPLIED MATHEMATICS, 2014,
[7] STABILITY AND BIFURCATION IN A PREDATOR-PREY MODEL WITH PREY REFUGE
Chen, Wenchang
Yu, Hengguo
Dai, Chuanjun
Guo, Qing
Liu, He
Zhao, Min
[J]. JOURNAL OF BIOLOGICAL SYSTEMS, 2023, 31 (02) : 417 - 435
[8] Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting
Guin, Lakshmi Narayan
Acharya, Sattwika
[J]. NONLINEAR DYNAMICS, 2017, 88 (02) : 1501 - 1533
[9] SPATIOTEMPORAL DYNAMICS OF A PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE
Sambath, M.
Balachandran, K.
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2013, 3 (01): : 71 - 80
[10] Dynamical response of a reaction-diffusion predator-prey system with cooperative hunting and prey refuge
Han, Renji
Mandal, Gourav
Guin, Akshmi Narayan
Chakravarty, Santabrata
[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2022, 2022 (10):

← 1 2 3 4 5 →