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Original Articles

Pattern formation in prey-taxis systems

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Pages 551-573 | Received 03 Jul 2007, Published online: 09 Oct 2009

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Read on this site (3)

Yongli Cai, Qian Cao & Zhi-An Wang. (2022) Asymptotic dynamics and spatial patterns of a ratio-dependent predator–prey system with prey-taxis. Applicable Analysis 101:1, pages 81-99.
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Sainan Wu & Wenjie Ni. (2021) Boundedness and global stability of a diffusive prey–predator model with prey-taxis. Applicable Analysis 100:15, pages 3259-3275.
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Articles from other publishers (112)

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Zhoumeng Xie & Yuxiang Li. (2024) Existence and qualitative analysis of a fully cross-diffusive predator-prey system with nonlinear taxis sensitivity. Journal of Differential Equations 380, pages 288-359.
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Dongxu Geng, Hao Wang, Weihua Jiang & Hongbin Wang. (2024) Double-Hopf bifurcation and Pattern Formation of a Gause-Kolmogorov-Type system with indirect prey-taxis and direct predator-taxis. Communications in Nonlinear Science and Numerical Simulation 128, pages 107647.
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Shanbing Li. (2023) Positive Steady-State Solutions for a Class of Prey-Predator Systems with Indirect Prey-Taxis. SIAM Journal on Mathematical Analysis 55:6, pages 6342-6374.
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Yan Li, Zhiyi Lv & Xiuzhen Fan. (2023) Bifurcations of a diffusive predator–prey model with prey‐stage structure and prey‐taxis. Mathematical Methods in the Applied Sciences 46:18, pages 18592-18604.
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Yujia Wang, Chuncheng Wang, Dejun Fan & Yuming Chen. (2023) Dynamics of a Predator–Prey Model with Memory-Based Diffusion. Journal of Dynamics and Differential Equations.
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Mykola Yaremenko. (2023) Aspects of Solvability Theory for Quasilinear Parabolic Systems in Specific Form with the Singular Coefficients. PROOF 3, pages 8-13.
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Lu Xu, Li Yang & Qiao Xin. (2023) Global boundedness for a food chain model with general logistic source. Journal of Mathematical Physics 64:7.
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Luhong Ye, Hongyong Zhao & Daiyong Wu. (2023) Spatial movement with memory-induced cross-diffusion effect and toxin effect in predator. Mathematics and Computers in Simulation.
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Purnedu Mishra & Dariusz Wrzosek. (2023) Pursuit-evasion dynamics for Bazykin-type predator-prey model with indirect predator taxis. Journal of Differential Equations 361, pages 391-416.
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Shanbing Li & Jianhua Wu. (2023) Global bifurcation of coexistence states for a prey-predator model with prey-taxis/predator-taxis. Advanced Nonlinear Studies 23:1.
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Demou Luo, Qiru Wang & Li Chen. (2023) Nonconstant steady states and pattern formations of generalized 1D cross‐diffusion systems with prey‐taxis. Studies in Applied Mathematics 150:3, pages 899-958.
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Jianping Wang & Mingxin Wang. (2023) Global solutions of a forager–exploiter model with nonlinear diffusions. Zeitschrift für angewandte Mathematik und Physik 74:2.
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Wenbin Lyu & Zhi‐An Wang. (2022) Global boundedness and asymptotics of a class of prey‐taxis models with singular response. Mathematical Methods in the Applied Sciences 46:6, pages 6705-6721.
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Youshan Tao & Michael Winkler. (2023) Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences, pages 1-36.
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Qingyan Shi & Yongli Song. (2023) Spatial movement with nonlocal memory. Discrete and Continuous Dynamical Systems - B 0:0, pages 0-0.
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Pan Zheng. (2023) Boundedness and global stability in a three-species predator-prey system with prey-taxis. Discrete and Continuous Dynamical Systems - B 0:0, pages 0-0.
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炎哲 韩. (2023) Property Analysis of Prey-Predator Model Based on Bazykin Functional Response Diffusion. Pure Mathematics 13:06, pages 1630-1642.
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Jianzhi Cao, Fang Li & Pengmiao Hao. (2022) Steady states of a diffusive predator-prey model with prey-taxis and fear effect. Boundary Value Problems 2022:1.
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Shanbing Li & Ruyun Ma. (2022) Positive steady-state solutions for predator–prey systems with prey-taxis and Dirichlet conditions. Nonlinear Analysis: Real World Applications 68, pages 103669.
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Qingyan Shi & Yongli Song. (2022) Spatially nonhomogeneous periodic patterns in a delayed predator–prey model with predator-taxis diffusion. Applied Mathematics Letters 131, pages 108062.
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Youshan Tao & Michael Winkler. (2022) Existence Theory and Qualitative Analysis for a Fully Cross-Diffusive Predator-Prey System. SIAM Journal on Mathematical Analysis 54:4, pages 4806-4864.
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Yingwei Song, Tie Zhang & Jinpeng Li. (2022) Dynamical behavior in a reaction-diffusion system with prey-taxis. Electronic Journal of Differential Equations 2022:01-87, pages 37.
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Mayra Núñez-López & Guillermo Chacón-Acosta. (2022) Pattern formation in a predator–prey system with a finite interaction range in a channel-like region using the Fick–Jacobs diffusion approach. Physica D: Nonlinear Phenomena 433, pages 133194.
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Sainan Wu. (2022) Global boundedness of a diffusive prey-predator model with indirect prey-taxis and predator-taxis. Journal of Mathematical Analysis and Applications 507:2, pages 125820.
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Wenbin Lyu. (2022) Boundedness and stabilization of a predator-prey model with attraction- repulsion taxis in all dimensions. Mathematical Biosciences and Engineering 19:12, pages 13458-13482.
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Pan Zheng. (2022) On a two-species competitive predator-prey system with density-dependent diffusion. Mathematical Biosciences and Engineering 19:12, pages 13421-13457.
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Chao Liu & Bin Liu. (2022) Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction. Discrete and Continuous Dynamical Systems - B 27:9, pages 4855.
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Hongfei Xu, Jinfeng Wang & Xuelian Xu. (2022) Dynamics and pattern formation in a cross-diffusion model with stage structure for predators. Discrete and Continuous Dynamical Systems - B 27:8, pages 4473.
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Qian Cao, Yongli Cai & Yong Luo. (2022) Nonconstant positive solutions to the ratio-dependent predator-prey system with prey-taxis in one dimension. Discrete & Continuous Dynamical Systems - B 27:3, pages 1397.
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Jianping Wang. (2022) Global solutions of a doubly tactic resource consumption model with logistic source. Journal of Mathematical Physics 63:1.
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Wenjie Zuo & Yongli Song. (2020) Stability and Double-Hopf Bifurcations of a Gause–Kolmogorov-Type Predator–Prey System with Indirect Prey-Taxis. Journal of Dynamics and Differential Equations 33:4, pages 1917-1957.
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Jie Xing, Pan Zheng & Xu Pan. (2021) A Quasilinear Predator-Prey Model with Indirect Prey-Taxis. Qualitative Theory of Dynamical Systems 20:3.
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Evan C. Haskell & Jonathan Bell. (2021) A model of the burglar alarm hypothesis of prey alarm calls. Theoretical Population Biology 141, pages 1-13.
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HAI-YANG JIN & ZHI-AN WANG. (2020) Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion. European Journal of Applied Mathematics 32:4, pages 652-682.
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Shuyan Qiu, Chunlai Mu & Xinyu Tu. (2021) Dynamics for a Three-Species Predator-Prey Model with Density-Dependent Motilities. Journal of Dynamics and Differential Equations.
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EVAN C. HASKELL & JONATHAN BELL. (2021) BIFURCATION ANALYSIS FOR A ONE PREDATOR AND TWO PREY MODEL WITH PREY-TAXIS. Journal of Biological Systems 29:02, pages 495-524.
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Demou Luo. (2021) Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis. Chaos, Solitons & Fractals 147, pages 110975.
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Jonathan Bell & Evan C. Haskell. (2021) Attraction–repulsion taxis mechanisms in a predator–prey model. Partial Differential Equations and Applications 2:3.
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Meijun Chen, Huaihuo Cao & Shengmao Fu. (2021) Stationary Patterns of a Predator–Prey Model with Prey-Stage Structure and Prey-Taxis. International Journal of Bifurcation and Chaos 31:03, pages 2150038.
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David Brown, Andrea Bruder & Miroslav Kummel. (2020) Endogenous spatial heterogeneity in a multi-patch predator-prey system: insights from a field-parameterized model. Theoretical Ecology 14:1, pages 107-122.
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Zefu Feng & Mei Zhang. (2021) Boundedness and large time behavior of solutions to a prey-taxis system accounting in liquid surrounding. Nonlinear Analysis: Real World Applications 57, pages 103197.
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Xinru Cao & Youshan Tao. (2021) Boundedness and stabilization enforced by mild saturation of taxis in a producer–scrounger model. Nonlinear Analysis: Real World Applications 57, pages 103189.
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Inkyung Ahn & Changwook Yoon. (2021) Global solvability of prey–predator models with indirect predator-taxis. Zeitschrift für angewandte Mathematik und Physik 72:1.
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Jing Li & Yifu Wang. (2021) Asymptotic behavior in a doubly tactic resource consumption model with proliferation. Zeitschrift für angewandte Mathematik und Physik 72:1.
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Guoshuang Wang & Jinfeng Wang. (2021) Pattern formation in predator prey systems with consuming resource and prey-taxis. Applied Mathematics Letters 111, pages 106681.
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Chunhua Jin. (2019) Periodic pattern formation in the coupled chemotaxis-(Navier–)Stokes system with mixed nonhomogeneous boundary conditions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150:6, pages 3121-3152.
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Purnedu Mishra & Dariusz Wrzosek. (2020) The role of indirect prey‐taxis and interference among predators in pattern formation. Mathematical Methods in the Applied Sciences 43:18, pages 10441-10461.
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Jianping Wang & Mingxin Wang. (2019) The Dynamics of a Predator–Prey Model with Diffusion and Indirect Prey-Taxis. Journal of Dynamics and Differential Equations 32:3, pages 1291-1310.
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Merlin C. Köhnke, Ivo Siekmann & Horst Malchow. (2020) Taxis-driven pattern formation in a predator-prey model with group defense. Ecological Complexity 43, pages 100848.
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Jianping Wang & Mingxin Wang. (2020) A predator–prey model with taxis mechanisms and stage structure for the predator. Nonlinearity 33:7, pages 3134-3172.
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Jinfeng Wang & Xinxin Guo. (2019) Dynamics and pattern formations in a three-species predator-prey model with two prey-taxis. Journal of Mathematical Analysis and Applications 475:2, pages 1054-1072.
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Lina Zhang & Shengmao Fu. (2019) Global bifurcation for a Holling–Tanner predator–prey model with prey-taxis. Nonlinear Analysis: Real World Applications 47, pages 460-472.
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