December  2008, 3(4): 863-879. doi: 10.3934/nhm.2008.3.863

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

1. 

Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Received  September 2007 Revised  January 2008 Published  October 2008

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. Networks and Heterogeneous Media, 2008, 3 (4) : 863-879. doi: 10.3934/nhm.2008.3.863
[1]

Guoqiang Ren, Bin Liu. Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 759-779. doi: 10.3934/dcds.2021136

[2]

Dan Li. Global stability in a multi-dimensional predator-prey system with prey-taxis. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1681-1705. doi: 10.3934/dcds.2020337

[3]

Qian Cao, Yongli Cai, Yong Luo. Nonconstant positive solutions to the ratio-dependent predator-prey system with prey-taxis in one dimension. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1397-1420. doi: 10.3934/dcdsb.2021095

[4]

Jinfeng Wang, Sainan Wu, Junping Shi. Pattern formation in diffusive predator-prey systems with predator-taxis and prey-taxis. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1273-1289. doi: 10.3934/dcdsb.2020162

[5]

Xin Wang, Ruijing Li, Yu Shi. Global generalized solutions to a three species predator-prey model with prey-taxis. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022031

[6]

Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057

[7]

Sebastién Gaucel, Michel Langlais. Some remarks on a singular reaction-diffusion system arising in predator-prey modeling. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 61-72. doi: 10.3934/dcdsb.2007.8.61

[8]

Evan C. Haskell, Jonathan Bell. Pattern formation in a predator-mediated coexistence model with prey-taxis. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 2895-2921. doi: 10.3934/dcdsb.2020045

[9]

Hengling Wang, Yuxiang Li. Boundedness in prey-taxis system with rotational flux terms. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4839-4851. doi: 10.3934/cpaa.2020214

[10]

Baifeng Zhang, Guohong Zhang, Xiaoli Wang. Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021260

[11]

Ke Wang, Qi Wang, Feng Yu. Stationary and time-periodic patterns of two-predator and one-prey systems with prey-taxis. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 505-543. doi: 10.3934/dcds.2017021

[12]

Hongmei Cheng, Rong Yuan. Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5433-5454. doi: 10.3934/dcds.2017236

[13]

Wenshu Zhou, Hongxing Zhao, Xiaodan Wei, Guokai Xu. Existence of positive steady states for a predator-prey model with diffusion. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2189-2201. doi: 10.3934/cpaa.2013.12.2189

[14]

Marcos Lizana, Julio Marín. On the dynamics of a ratio dependent Predator-Prey system with diffusion and delay. Discrete and Continuous Dynamical Systems - B, 2006, 6 (6) : 1321-1338. doi: 10.3934/dcdsb.2006.6.1321

[15]

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

[16]

Hongyong Zhao, Daiyong Wu. Point to point traveling wave and periodic traveling wave induced by Hopf bifurcation for a diffusive predator-prey system. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3271-3284. doi: 10.3934/dcdss.2020129

[17]

Jing-An Cui, Xinyu Song. Permanence of predator-prey system with stage structure. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 547-554. doi: 10.3934/dcdsb.2004.4.547

[18]

Dongmei Xiao, Kate Fang Zhang. Multiple bifurcations of a predator-prey system. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 417-433. doi: 10.3934/dcdsb.2007.8.417

[19]

Yun Kang, Sourav Kumar Sasmal, Amiya Ranjan Bhowmick, Joydev Chattopadhyay. Dynamics of a predator-prey system with prey subject to Allee effects and disease. Mathematical Biosciences & Engineering, 2014, 11 (4) : 877-918. doi: 10.3934/mbe.2014.11.877

[20]

Xinyu Song, Liming Cai, U. Neumann. Ratio-dependent predator-prey system with stage structure for prey. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 747-758. doi: 10.3934/dcdsb.2004.4.747

2021 Impact Factor: 1.41

Metrics

  • PDF downloads (121)
  • HTML views (0)
  • Cited by (16)

Other articles
by authors

[Back to Top]