Search Advanced

Networks and Heterogeneous Media

2008, Volume 3, Issue 4: 863-879. doi: 10.3934/nhm.2008.3.863
Previous Article Next Article

Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis

  • 1.
    Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción
  • Received: 01 September 2007 Revised: 01 January 2008

  • Primary: 35K57, 35K55, 92B05

  • In this paper, we consider a system of nonlinear partial differential equations modeling the Lotka Volterra interactions of preys and actively moving predators with prey-taxis and spatial diffusion. The interaction between predators are modelized by the statement of a food pyramid condition. We establish the existence of weak solutions by using Schauder fixed-point theorem and uniqueness via duality technique. This paper is a generalization of the results obtained in [2].

    Citation: Mostafa Bendahmane. Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis[J]. Networks and Heterogeneous Media, 2008, 3(4): 863-879. doi: 10.3934/nhm.2008.3.863

    Related Papers:

    [1] Mostafa Bendahmane . Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis. Networks and Heterogeneous Media, 2008, 3(4): 863-879. doi: 10.3934/nhm.2008.3.863
    [2] Verónica Anaya, Mostafa Bendahmane, Mauricio Sepúlveda . Mathematical and numerical analysis for Predator-prey system in a polluted environment. Networks and Heterogeneous Media, 2010, 5(4): 813-847. doi: 10.3934/nhm.2010.5.813
    [3] Rinaldo M. Colombo, Francesca Marcellini, Elena Rossi . Biological and industrial models motivating nonlocal conservation laws: A review of analytic and numerical results. Networks and Heterogeneous Media, 2016, 11(1): 49-67. doi: 10.3934/nhm.2016.11.49
    [4] Simone Fagioli, Yahya Jaafra . Multiple patterns formation for an aggregation/diffusion predator-prey system. Networks and Heterogeneous Media, 2021, 16(3): 377-411. doi: 10.3934/nhm.2021010
    [5] Verónica Anaya, Mostafa Bendahmane, David Mora, Ricardo Ruiz Baier . On a vorticity-based formulation for reaction-diffusion-Brinkman systems. Networks and Heterogeneous Media, 2018, 13(1): 69-94. doi: 10.3934/nhm.2018004
    [6] Mostafa Bendahmane, Kenneth H. Karlsen . Martingale solutions of stochastic nonlocal cross-diffusion systems. Networks and Heterogeneous Media, 2022, 17(5): 719-752. doi: 10.3934/nhm.2022024
    [7] Mostafa Bendahmane, Kenneth H. Karlsen . Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Networks and Heterogeneous Media, 2006, 1(1): 185-218. doi: 10.3934/nhm.2006.1.185
    [8] Narcisa Apreutesei, Vitaly Volpert . Reaction-diffusion waves with nonlinear boundary conditions. Networks and Heterogeneous Media, 2013, 8(1): 23-35. doi: 10.3934/nhm.2013.8.23
    [9] Don A. Jones, Hal L. Smith, Horst R. Thieme . Spread of viral infection of immobilized bacteria. Networks and Heterogeneous Media, 2013, 8(1): 327-342. doi: 10.3934/nhm.2013.8.327
    [10] Toshiyuki Ogawa, Takashi Okuda . Oscillatory dynamics in a reaction-diffusion system in the presence of 0:1:2 resonance. Networks and Heterogeneous Media, 2012, 7(4): 893-926. doi: 10.3934/nhm.2012.7.893
  • In this paper, we consider a system of nonlinear partial differential equations modeling the Lotka Volterra interactions of preys and actively moving predators with prey-taxis and spatial diffusion. The interaction between predators are modelized by the statement of a food pyramid condition. We establish the existence of weak solutions by using Schauder fixed-point theorem and uniqueness via duality technique. This paper is a generalization of the results obtained in [2].


  • This article has been cited by:

    1. Jonathan Bell, Evan C. Haskell, Attraction–repulsion taxis mechanisms in a predator–prey model, 2021, 2, 2662-2963, 10.1007/s42985-021-00080-0
    2. Mostafa Bendahmane, Kenneth H. Karlsen, Martingale solutions of stochastic nonlocal cross-diffusion systems, 2022, 17, 1556-1801, 719, 10.3934/nhm.2022024
    3. A. N. Elmurodov, M. S. Rasulov, On a Uniqueness of Solution for a Reaction-Diffusion Type System with a Free Boundary, 2022, 43, 1995-0802, 2099, 10.1134/S1995080222110087
    4. Youshan Tao, Global existence of classical solutions to a predator–prey model with nonlinear prey-taxis, 2010, 11, 14681218, 2056, 10.1016/j.nonrwa.2009.05.005
    5. Lakshmi Narayan Guin, Mainul Haque, Prashanta Kumar Mandal, The spatial patterns through diffusion-driven instability in a predator–prey model, 2012, 36, 0307904X, 1825, 10.1016/j.apm.2011.05.055
    6. Mostafa Bendahmane, Michel Langlais, A reaction-diffusion system with cross-diffusion modeling the spread of an epidemic disease, 2010, 10, 1424-3199, 883, 10.1007/s00028-010-0074-y
    7. L. Shangerganesh, N. Barani Balan, K. Balachandran, Weak-renormalized solutions for predator–prey system, 2013, 92, 0003-6811, 441, 10.1080/00036811.2011.625014
    8. Dietmar Hömberg, Robert Lasarzik, Luisa Plato, On the existence of generalized solutions to a spatio-temporal predator–prey system with prey-taxis, 2023, 23, 1424-3199, 10.1007/s00028-023-00871-5
    9. Chenglin Li, Global existence of classical solutions to the cross-diffusion three-species model with prey-taxis, 2016, 72, 08981221, 1394, 10.1016/j.camwa.2016.07.002
    10. Huanhuan Qiu, Shangjiang Guo, Shangzhi Li, Stability and Bifurcation in a Predator–Prey System with Prey-Taxis, 2020, 30, 0218-1274, 2050022, 10.1142/S0218127420500224
    11. Sainan Wu, Junping Shi, Boying Wu, Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis, 2016, 260, 00220396, 5847, 10.1016/j.jde.2015.12.024
    12. EVAN C. HASKELL, JONATHAN BELL, BIFURCATION ANALYSIS FOR A ONE PREDATOR AND TWO PREY MODEL WITH PREY-TAXIS, 2021, 29, 0218-3390, 495, 10.1142/S0218339021400131
    13. Mostafa Bendahmane, Weak and classical solutions to predator–prey system with cross-diffusion, 2010, 73, 0362546X, 2489, 10.1016/j.na.2010.06.021
    14. Lakshmi Narayan Guin, Existence of spatial patterns in a predator–prey model with self- and cross-diffusion, 2014, 226, 00963003, 320, 10.1016/j.amc.2013.10.005
    15. Jianping Gao, Shangjiang Guo, Effect of prey-taxis and diffusion on positive steady states for a predator-prey system, 2018, 41, 01704214, 3570, 10.1002/mma.4847
    16. Xiaoli Wang, Wendi Wang, Guohong Zhang, Global bifurcation of solutions for a predator-prey model with prey-taxis, 2015, 38, 01704214, 431, 10.1002/mma.3079
    17. Wendkouni Ouedraogo, Hamidou Ouedraogo, Boureima Sangaré, A Reaction Diffusion Model to Describe the Toxin Effect on the Fish-Plankton Population, 2018, 2018, 2314-4629, 1, 10.1155/2018/2037093
    18. Gurusamy Arumugam, Global existence and stability of three species predator-prey system with prey-taxis, 2023, 20, 1551-0018, 8448, 10.3934/mbe.2023371
    19. Alaaeddine Hammoudi, Oana Iosifescu, Mathematical Analysis of a Chemotaxis-Type Model of Soil Carbon Dynamic, 2018, 39, 0252-9599, 253, 10.1007/s11401-018-1063-7
    20. Yan Jiang, Intermittent distributed control for a class of nonlinear reaction-diffusion systems with spatial point measurements, 2019, 356, 00160032, 3811, 10.1016/j.jfranklin.2019.01.010
    21. Verónica Anaya, Mostafa Bendahmane, Michel Langlais, Mauricio Sepúlveda, A convergent finite volume method for a model of indirectly transmitted diseases with nonlocal cross-diffusion, 2015, 70, 08981221, 132, 10.1016/j.camwa.2015.04.021
    22. Chenglin Li, Zhangguo Hong, Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes, 2012, 2012, 1110-757X, 1, 10.1155/2012/702603
    23. Yan Li, Zhiyi Lv, Fengrong Zhang, Hui Hao, Bifurcation analysis of a diffusive predator–prey model with hyperbolic mortality and prey-taxis, 2024, 17, 1793-5245, 10.1142/S1793524523500110
  • Reader Comments
  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.8

Metrics

Article views(4468) PDF downloads(133) Cited by(23)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog