Coexistence states of a predator-prey model with cross-diffusion

被引：11
|
作者：
Yuan, Hailong [1 ]
Wu, Jianhua [1 ]
Jia, Yunfeng [1 ]
Nie, Hua [1 ]
机构：
[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Shaanxi, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 41卷
关键词：
Predator-prey model; Cross-diffusion; Coexistence states; Multiplicity; Bifurcation; POSITIVE STEADY-STATES; GLOBAL BIFURCATION; PROTECTION ZONE; SYSTEM; EQUATIONS;
D O I：
10.1016/j.nonrwa.2017.10.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with positive solutions of a predator-prey model with cross diffusion. By virtue of the Leray-Schauder degree theory and the bifurcation theory, some sufficient conditions for the existence of positive solutions of the system are established. In particular, we derive the multiplicity results when some parameters are suitably large. Moreover, the existence and stability of nonconstant solutions are studied by the techniques of space decomposition and the implicit function theorem. Finally, the uniqueness of positive solution is studied when the spatial dimension is one. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：179 / 203
页数：25
相关论文
共 50 条
  • [31] Bifurcation and turing instability for a predator-prey model with nonlinear reaction cross-diffusion
    Cao, Jianzhi
    Sun, Hongyan
    Hao, Pengmiao
    Wang, Peiguang
    APPLIED MATHEMATICAL MODELLING, 2021, 89 : 1663 - 1677
  • [32] Pattern dynamics of a cross-diffusion predator-prey model with nonlinear harvesting term
    Lian, Xinze
    Wu, Huihui
    Zhu, Meng
    Xu, Weimin
    ADVANCES IN CONTINUOUS AND DISCRETE MODELS, 2025, 2025 (01):
  • [33] Global attractor for a three-species predator-prey model with cross-diffusion
    Guo, Haojie
    Zheng, Sining
    MATHEMATISCHE NACHRICHTEN, 2011, 284 (17-18) : 2175 - 2183
  • [34] Cross-diffusion induced spatiotemporal patterns in a predator-prey model with herd behavior
    Tang, Xiaosong
    Song, Yongli
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 24 : 36 - 49
  • [35] Stability analysis of predator-prey models involving cross-diffusion
    Ferreira, Jocirei D.
    da Silva, Severino Horacio
    Rao, V. Sree Hari
    PHYSICA D-NONLINEAR PHENOMENA, 2019, 400
  • [36] Pattern formation induced by cross-diffusion in a predator-prey system
    孙桂全
    靳祯
    刘权兴
    李莉
    Chinese Physics B, 2008, (11) : 3936 - 3941
  • [37] Global Solutions for a General Predator-Prey Model with Prey-Stage Structure and Cross-Diffusion
    Li, Xiaojuan
    Xu, Shenghu
    FILOMAT, 2022, 36 (07) : 2153 - 2170
  • [38] Spatial Pattern of Ratio-Dependent Predator-Prey Model with Prey Harvesting and Cross-Diffusion
    Sivasamy, R.
    Sivakumar, M.
    Balachandran, K.
    Sathiyanathan, K.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2019, 29 (03):
  • [39] Pattern formation induced by cross-diffusion in a predator-prey system
    Sun Gui-Quan
    Jin Zhen
    Liu Quan-Xing
    Li Li
    CHINESE PHYSICS B, 2008, 17 (11) : 3936 - 3941
  • [40] Weak and classical solutions to predator-prey system with cross-diffusion
    Bendahmane, Mostafa
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (08) : 2489 - 2503
12345