Dynamic and pattern formation of a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis
This paper is concerned with a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis, which describes the interaction between the predator and the prey. It means that the predator is attracted to the chemical excreted by prey, meanwhile, the prey is repelled to the chemi...
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| Published in | Nonlinear analysis: real world applications Vol. 84; p. 104299 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.08.2025
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| Online Access | Get full text |
| ISSN | 1468-1218 |
| DOI | 10.1016/j.nonrwa.2024.104299 |
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| Abstract | This paper is concerned with a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis, which describes the interaction between the predator and the prey. It means that the predator is attracted to the chemical excreted by prey, meanwhile, the prey is repelled to the chemical excreted by predator. The linear stability of constant steady states to the system is obtained. We prove the existence of Hopf bifurcations by choosing the indirect predator-taxis coefficient as the bifurcation parameter and find that both the indirect prey-taxis and indirect predator-taxis promote the system to produce more complex spatiotemporal patterns. Through the bifurcation theory, the existence of steady state bifurcations is established. Moreover, we show the global stability of the semi-trivial steady state and positive constant steady state. Finally, we use numerical examples to check the theoretical results and gain the spatiotemporal patterns. |
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| AbstractList | This paper is concerned with a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis, which describes the interaction between the predator and the prey. It means that the predator is attracted to the chemical excreted by prey, meanwhile, the prey is repelled to the chemical excreted by predator. The linear stability of constant steady states to the system is obtained. We prove the existence of Hopf bifurcations by choosing the indirect predator-taxis coefficient as the bifurcation parameter and find that both the indirect prey-taxis and indirect predator-taxis promote the system to produce more complex spatiotemporal patterns. Through the bifurcation theory, the existence of steady state bifurcations is established. Moreover, we show the global stability of the semi-trivial steady state and positive constant steady state. Finally, we use numerical examples to check the theoretical results and gain the spatiotemporal patterns. |
| ArticleNumber | 104299 |
| Author | Wang, Yiran Wu, Sainan Geng, Dongxu |
| Author_xml | – sequence: 1 givenname: Sainan orcidid: 0000-0002-8268-5925 surname: Wu fullname: Wu, Sainan email: wusn@njupt.edu.cn – sequence: 2 givenname: Yiran surname: Wang fullname: Wang, Yiran – sequence: 3 givenname: Dongxu surname: Geng fullname: Geng, Dongxu |
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| Cites_doi | 10.1086/282272 10.3934/dcdsb.2023060 10.1142/S0218202518400158 10.1080/17513750802716112 10.1126/science.171.3969.385 10.1016/j.jde.2008.10.024 10.1086/284707 10.1007/s00285-010-0332-1 10.1002/mma.3079 10.3934/dcdsb.2021240 10.1016/j.jde.2019.10.019 10.1016/j.nonrwa.2007.06.017 10.1007/s00033-020-01461-y 10.1007/s00028-023-00931-w 10.1016/j.jde.2016.10.010 10.1016/j.jde.2023.02.063 10.1016/j.cnsns.2023.107647 10.1016/j.jmaa.2024.128948 10.1007/s10884-019-09778-7 10.3934/eect.2024015 10.1016/j.nonrwa.2009.05.005 10.1016/j.aml.2015.04.017 10.1142/S0218202516400108 10.1016/j.jde.2015.12.024 10.1142/S0218202522500014 10.1016/j.jmaa.2021.125820 10.3934/dcdsb.2015.20.3165 10.1016/j.jde.2008.09.009 |
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| Keywords | 92D25 35B35 Global stability Indirect predator-taxis Nonconstant steady state solution Indirect prey-taxis Periodic solution Predator–prey model Spatiotemporal pattern 35K55 35Q92 |
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| References | Ladyzenskaja, Solonnikov, Ural’ceva (b33) 1967 Mishra, Wrzosek (b25) 2023; 361 Rosenzweig (b2) 1971; 171 Qi, Ke (b27) 2022; 27 Zhang, Zhang, Xin (b23) 2025; 543 Murray (b1) 2002; vol. 17 Wu, Ni (b15) 2020 Zheng, Liu, Zhang (b29) 2023; 28 Wu, Shi, Wu (b14) 2016; 260 Mishra, Wrzosek (b22) 2022; 32 Lee, Hillen, Lewis (b9) 2009; 3 Kareiva, Odell (b6) 1987; 130 Liu, Shi, Wang (b31) 2013; 18 Ahn, Yoon (b21) 2021; 72 Zhang, Zhang, Xin (b24) 2024; 13 Wu, Wang, Shi (b7) 2018; 28 Ainseba, Bendahmane, Noussair (b8) 2008; 9 Jin, Wang (b13) 2017; 262 Wang, Wu, Shi (b16) 2021; 26 Wan, Zheng, Shan (b28) 2023; 23 Shi, Wang (b32) 2009; 246 Wang, Wang, Zhang (b11) 2015; 38 Wu (b26) 2022; 507 Yi, Wei, Shi (b4) 2009; 246 Xiao, Zheng (b12) 2015; 49 Tao, Winkler (b30) 2015; 20 Wang, Wang (b18) 2020; 32 Geng, Wang, Jiang, Wang (b20) 2024; 128 Tello, Wrzosek (b17) 2016; 26 Wang, Shi, Wei (b5) 2011; 62 Ahn, Yoon (b19) 2020; 268 Rosenzweig, MacArthur (b3) 1963; 97 Tao (b10) 2010; 11 Wu (10.1016/j.nonrwa.2024.104299_b26) 2022; 507 Ahn (10.1016/j.nonrwa.2024.104299_b21) 2021; 72 Wang (10.1016/j.nonrwa.2024.104299_b18) 2020; 32 Wang (10.1016/j.nonrwa.2024.104299_b11) 2015; 38 Ahn (10.1016/j.nonrwa.2024.104299_b19) 2020; 268 Kareiva (10.1016/j.nonrwa.2024.104299_b6) 1987; 130 Yi (10.1016/j.nonrwa.2024.104299_b4) 2009; 246 Jin (10.1016/j.nonrwa.2024.104299_b13) 2017; 262 Wan (10.1016/j.nonrwa.2024.104299_b28) 2023; 23 Tello (10.1016/j.nonrwa.2024.104299_b17) 2016; 26 Zheng (10.1016/j.nonrwa.2024.104299_b29) 2023; 28 Wang (10.1016/j.nonrwa.2024.104299_b16) 2021; 26 Shi (10.1016/j.nonrwa.2024.104299_b32) 2009; 246 Liu (10.1016/j.nonrwa.2024.104299_b31) 2013; 18 Xiao (10.1016/j.nonrwa.2024.104299_b12) 2015; 49 Mishra (10.1016/j.nonrwa.2024.104299_b25) 2023; 361 Tao (10.1016/j.nonrwa.2024.104299_b30) 2015; 20 Wang (10.1016/j.nonrwa.2024.104299_b5) 2011; 62 Wu (10.1016/j.nonrwa.2024.104299_b7) 2018; 28 Rosenzweig (10.1016/j.nonrwa.2024.104299_b3) 1963; 97 Zhang (10.1016/j.nonrwa.2024.104299_b23) 2025; 543 Zhang (10.1016/j.nonrwa.2024.104299_b24) 2024; 13 Ainseba (10.1016/j.nonrwa.2024.104299_b8) 2008; 9 Wu (10.1016/j.nonrwa.2024.104299_b15) 2020 Qi (10.1016/j.nonrwa.2024.104299_b27) 2022; 27 Murray (10.1016/j.nonrwa.2024.104299_b1) 2002; vol. 17 Lee (10.1016/j.nonrwa.2024.104299_b9) 2009; 3 Mishra (10.1016/j.nonrwa.2024.104299_b22) 2022; 32 Rosenzweig (10.1016/j.nonrwa.2024.104299_b2) 1971; 171 Tao (10.1016/j.nonrwa.2024.104299_b10) 2010; 11 Wu (10.1016/j.nonrwa.2024.104299_b14) 2016; 260 Geng (10.1016/j.nonrwa.2024.104299_b20) 2024; 128 Ladyzenskaja (10.1016/j.nonrwa.2024.104299_b33) 1967 |
| References_xml | – volume: 62 start-page: 291 year: 2011 end-page: 331 ident: b5 article-title: Predator-prey system with strong Allee effect in prey publication-title: J. Math. Biol. – volume: 11 start-page: 2056 year: 2010 end-page: 2064 ident: b10 article-title: Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis publication-title: Nonlinear Anal. Real World Appl. – volume: 128 start-page: 22 year: 2024 ident: b20 article-title: Double-hopf bifurcation and pattern formation of a Gause-Kolmogorov-type system with indirect prey-taxis and direct predator-taxis publication-title: Commun. Nonlinear Sci. Numer. Simul. – volume: 32 start-page: 1291 year: 2020 end-page: 1310 ident: b18 article-title: The dynamic of a predator-prey model with diffusion and indirect prey-taxis publication-title: J. Dyn. Differ. Equ. – volume: 26 start-page: 2129 year: 2016 end-page: 2162 ident: b17 article-title: Predator-prey model with diffusion and indirect prey-taxis publication-title: Math. Models Methods Appl. Sci. – volume: 171 start-page: 385 year: 1971 end-page: 387 ident: b2 article-title: Paradox of enrichment: destabilization of exploitation ecosystems in ecological time publication-title: Science – volume: 26 start-page: 1273 year: 2021 end-page: 1289 ident: b16 article-title: Pattern formation in diffusive predator-prey systems with predator-taxis and prey-taxis publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 49 start-page: 73 year: 2015 end-page: 77 ident: b12 article-title: Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis publication-title: Appl. Math. Lett. – volume: 3 start-page: 551 year: 2009 end-page: 573 ident: b9 article-title: Pattern formation in prey-taxis systems publication-title: J. Biol. Dyn. – volume: 72 year: 2021 ident: b21 article-title: Global solvability of prey-predator models with indirect predator-taxis publication-title: Z. Angew. Math. Phys. – volume: 32 start-page: 1 year: 2022 end-page: 42 ident: b22 article-title: Repulsive chemotaxis and predator evasion in predator-prey models with diffusion and prey-taxis publication-title: Math. Models Methods Appl. Sci. – volume: 262 start-page: 1257 year: 2017 end-page: 1290 ident: b13 article-title: Global stability of prey-taxis systems publication-title: J. Differential Equations – volume: 246 start-page: 2788 year: 2009 end-page: 2812 ident: b32 article-title: On global bifurcation for quasilinear elliptic systems on bounded domains publication-title: J. Differential Equations – start-page: 736 year: 1967 ident: b33 article-title: Linear and quasi-linear equations of parabolic type – volume: 97 start-page: 209 year: 1963 end-page: 223 ident: b3 article-title: Graphical representation and stability conditions of predator-prey interactions publication-title: Amer. Nat. – volume: 507 start-page: 21 year: 2022 ident: b26 article-title: Global boundedness of a diffusive prey-predator model with indirect prey-taxis and predator-taxis publication-title: J. Math. Anal. Appl. – volume: 268 start-page: 4222 year: 2020 end-page: 4255 ident: b19 article-title: Global well-posedness and stability analysis of prey-predator model with indirect prey-taxis publication-title: J. Differential Equations – volume: 23 start-page: 39 year: 2023 ident: b28 article-title: On a quasilinear fully parabolic predator-prey model with indirect pursuit-evasion interaction publication-title: J. Evol. Equ. – volume: 20 start-page: 3165 year: 2015 end-page: 3183 ident: b30 article-title: Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 543 start-page: 28 year: 2025 ident: b23 article-title: Dynamic behavior in a pursuit-evasion system with signaling mechanism publication-title: J. Math. Anal. Appl. – volume: 9 start-page: 2086 year: 2008 end-page: 2105 ident: b8 article-title: A reaction-diffusion system modeling predator-prey with prey-taxis publication-title: Nonlinear Anal. Real World Appl. – volume: 361 start-page: 391 year: 2023 end-page: 416 ident: b25 article-title: Pursuit-evasion dynamics for bazykin-type predator-prey model with indirect predator taxis publication-title: J. Differential Equations – volume: 130 start-page: 233 year: 1987 end-page: 270 ident: b6 article-title: Swarms of predators exhibit “preytaxis” if individual predators use area-restricted search publication-title: Amer. Nat. – volume: vol. 17 start-page: xxiv+551 year: 2002 ident: b1 publication-title: Mathematical Biology. I – year: 2020 ident: b15 article-title: Boundedness and global stability of a diffusive prey-predator model with prey-taxis publication-title: Appl. Anal. – volume: 260 start-page: 5847 year: 2016 end-page: 5874 ident: b14 article-title: Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis publication-title: J. Differential Equations – volume: 27 start-page: 4531 year: 2022 end-page: 4549 ident: b27 article-title: Large time behavior in a predator-prey system with pursuit-evasion interaction publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 38 start-page: 431 year: 2015 end-page: 443 ident: b11 article-title: Global bifurcation of solutions for a predator-prey model with prey-taxis publication-title: Math. Methods Appl. Sci. – volume: 13 start-page: 1015 year: 2024 end-page: 1037 ident: b24 article-title: Global dynamics of bazykin-type cross-diffusive model with indirect predator-taxis publication-title: Evol. Equ. Control Theory – volume: 28 start-page: 2275 year: 2018 end-page: 2312 ident: b7 article-title: Dynamics and pattern formation of a diffusive predator-prey model with predator-taxis publication-title: Math. Models Methods Appl. Sci. – volume: 246 start-page: 1944 year: 2009 end-page: 1977 ident: b4 article-title: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system publication-title: J. Differential Equations – volume: 28 start-page: 5437 year: 2023 end-page: 5446 ident: b29 article-title: Existence and boundedness of solutions for a parabolic-elliptic predator-prey chemotaxis system publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 18 start-page: 2597 year: 2013 end-page: 2625 ident: b31 article-title: Pattern formation of the attraction-repulsion Keller-Segel system publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 97 start-page: 209 year: 1963 ident: 10.1016/j.nonrwa.2024.104299_b3 article-title: Graphical representation and stability conditions of predator-prey interactions publication-title: Amer. Nat. doi: 10.1086/282272 – volume: 28 start-page: 5437 issue: 11 year: 2023 ident: 10.1016/j.nonrwa.2024.104299_b29 article-title: Existence and boundedness of solutions for a parabolic-elliptic predator-prey chemotaxis system publication-title: Discrete Contin. Dyn. Syst. Ser. B doi: 10.3934/dcdsb.2023060 – volume: 28 start-page: 2275 issue: 11 year: 2018 ident: 10.1016/j.nonrwa.2024.104299_b7 article-title: Dynamics and pattern formation of a diffusive predator-prey model with predator-taxis publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202518400158 – volume: 3 start-page: 551 issue: 6 year: 2009 ident: 10.1016/j.nonrwa.2024.104299_b9 article-title: Pattern formation in prey-taxis systems publication-title: J. Biol. Dyn. doi: 10.1080/17513750802716112 – volume: 171 start-page: 385 issue: 3969 year: 1971 ident: 10.1016/j.nonrwa.2024.104299_b2 article-title: Paradox of enrichment: destabilization of exploitation ecosystems in ecological time publication-title: Science doi: 10.1126/science.171.3969.385 – volume: 246 start-page: 1944 issue: 5 year: 2009 ident: 10.1016/j.nonrwa.2024.104299_b4 article-title: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system publication-title: J. Differential Equations doi: 10.1016/j.jde.2008.10.024 – volume: 130 start-page: 233 issue: 2 year: 1987 ident: 10.1016/j.nonrwa.2024.104299_b6 article-title: Swarms of predators exhibit “preytaxis” if individual predators use area-restricted search publication-title: Amer. Nat. doi: 10.1086/284707 – volume: 62 start-page: 291 issue: 3 year: 2011 ident: 10.1016/j.nonrwa.2024.104299_b5 article-title: Predator-prey system with strong Allee effect in prey publication-title: J. Math. Biol. doi: 10.1007/s00285-010-0332-1 – volume: 38 start-page: 431 year: 2015 ident: 10.1016/j.nonrwa.2024.104299_b11 article-title: Global bifurcation of solutions for a predator-prey model with prey-taxis publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3079 – volume: 27 start-page: 4531 issue: 8 year: 2022 ident: 10.1016/j.nonrwa.2024.104299_b27 article-title: Large time behavior in a predator-prey system with pursuit-evasion interaction publication-title: Discrete Contin. Dyn. Syst. Ser. B doi: 10.3934/dcdsb.2021240 – volume: 268 start-page: 4222 issue: 8 year: 2020 ident: 10.1016/j.nonrwa.2024.104299_b19 article-title: Global well-posedness and stability analysis of prey-predator model with indirect prey-taxis publication-title: J. Differential Equations doi: 10.1016/j.jde.2019.10.019 – volume: 9 start-page: 2086 issue: 5 year: 2008 ident: 10.1016/j.nonrwa.2024.104299_b8 article-title: A reaction-diffusion system modeling predator-prey with prey-taxis publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2007.06.017 – year: 2020 ident: 10.1016/j.nonrwa.2024.104299_b15 article-title: Boundedness and global stability of a diffusive prey-predator model with prey-taxis publication-title: Appl. Anal. – volume: 18 start-page: 2597 issue: 10 year: 2013 ident: 10.1016/j.nonrwa.2024.104299_b31 article-title: Pattern formation of the attraction-repulsion Keller-Segel system publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 72 issue: 1 year: 2021 ident: 10.1016/j.nonrwa.2024.104299_b21 article-title: Global solvability of prey-predator models with indirect predator-taxis publication-title: Z. Angew. Math. Phys. doi: 10.1007/s00033-020-01461-y – volume: 23 start-page: 39 issue: 4 year: 2023 ident: 10.1016/j.nonrwa.2024.104299_b28 article-title: On a quasilinear fully parabolic predator-prey model with indirect pursuit-evasion interaction publication-title: J. Evol. Equ. doi: 10.1007/s00028-023-00931-w – volume: 262 start-page: 1257 issue: 3 year: 2017 ident: 10.1016/j.nonrwa.2024.104299_b13 article-title: Global stability of prey-taxis systems publication-title: J. Differential Equations doi: 10.1016/j.jde.2016.10.010 – volume: 361 start-page: 391 year: 2023 ident: 10.1016/j.nonrwa.2024.104299_b25 article-title: Pursuit-evasion dynamics for bazykin-type predator-prey model with indirect predator taxis publication-title: J. Differential Equations doi: 10.1016/j.jde.2023.02.063 – volume: 128 start-page: 22 year: 2024 ident: 10.1016/j.nonrwa.2024.104299_b20 article-title: Double-hopf bifurcation and pattern formation of a Gause-Kolmogorov-type system with indirect prey-taxis and direct predator-taxis publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2023.107647 – volume: 543 start-page: 28 issue: 2 year: 2025 ident: 10.1016/j.nonrwa.2024.104299_b23 article-title: Dynamic behavior in a pursuit-evasion system with signaling mechanism publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2024.128948 – volume: 32 start-page: 1291 year: 2020 ident: 10.1016/j.nonrwa.2024.104299_b18 article-title: The dynamic of a predator-prey model with diffusion and indirect prey-taxis publication-title: J. Dyn. Differ. Equ. doi: 10.1007/s10884-019-09778-7 – volume: 13 start-page: 1015 issue: 4 year: 2024 ident: 10.1016/j.nonrwa.2024.104299_b24 article-title: Global dynamics of bazykin-type cross-diffusive model with indirect predator-taxis publication-title: Evol. Equ. Control Theory doi: 10.3934/eect.2024015 – volume: 26 start-page: 1273 issue: 3 year: 2021 ident: 10.1016/j.nonrwa.2024.104299_b16 article-title: Pattern formation in diffusive predator-prey systems with predator-taxis and prey-taxis publication-title: Discrete Contin. Dyn. Syst. Ser. B – volume: 11 start-page: 2056 issue: 3 year: 2010 ident: 10.1016/j.nonrwa.2024.104299_b10 article-title: Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2009.05.005 – volume: 49 start-page: 73 year: 2015 ident: 10.1016/j.nonrwa.2024.104299_b12 article-title: Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2015.04.017 – volume: 26 start-page: 2129 issue: 11 year: 2016 ident: 10.1016/j.nonrwa.2024.104299_b17 article-title: Predator-prey model with diffusion and indirect prey-taxis publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202516400108 – volume: vol. 17 start-page: xxiv+551 year: 2002 ident: 10.1016/j.nonrwa.2024.104299_b1 – start-page: 736 year: 1967 ident: 10.1016/j.nonrwa.2024.104299_b33 – volume: 260 start-page: 5847 issue: 7 year: 2016 ident: 10.1016/j.nonrwa.2024.104299_b14 article-title: Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis publication-title: J. Differential Equations doi: 10.1016/j.jde.2015.12.024 – volume: 32 start-page: 1 issue: 1 year: 2022 ident: 10.1016/j.nonrwa.2024.104299_b22 article-title: Repulsive chemotaxis and predator evasion in predator-prey models with diffusion and prey-taxis publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202522500014 – volume: 507 start-page: 21 issue: 2 year: 2022 ident: 10.1016/j.nonrwa.2024.104299_b26 article-title: Global boundedness of a diffusive prey-predator model with indirect prey-taxis and predator-taxis publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2021.125820 – volume: 20 start-page: 3165 issue: 9 year: 2015 ident: 10.1016/j.nonrwa.2024.104299_b30 article-title: Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals publication-title: Discrete Contin. Dyn. Syst. Ser. B doi: 10.3934/dcdsb.2015.20.3165 – volume: 246 start-page: 2788 issue: 7 year: 2009 ident: 10.1016/j.nonrwa.2024.104299_b32 article-title: On global bifurcation for quasilinear elliptic systems on bounded domains publication-title: J. Differential Equations doi: 10.1016/j.jde.2008.09.009 |
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| StartPage | 104299 |
| SubjectTerms | Global stability Indirect predator-taxis Indirect prey-taxis Nonconstant steady state solution Periodic solution Predator–prey model Spatiotemporal pattern |
| Title | Dynamic and pattern formation of a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis |
| URI | https://dx.doi.org/10.1016/j.nonrwa.2024.104299 |
| Volume | 84 |
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