Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response
This paper is concerned with a modified Leslie–Gower predator–prey diffusive dynamics system with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is Beddington–DeAngelis (Denote it by B–D) functional response term. Firstly, by applying the theory of s...
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| Published in | Chaos, solitons and fractals Vol. 174; p. 113794 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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01.09.2023
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| Abstract | This paper is concerned with a modified Leslie–Gower predator–prey diffusive dynamics system with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is Beddington–DeAngelis (Denote it by B–D) functional response term. Firstly, by applying the theory of stability and the Hopf bifurcation, we discuss the local stability and the existence of the Hopf bifurcation at the positive constant equilibrium solution of the ODE model, which the model undergoes the Hopf bifurcation when bifurcation parameter δ crosses the bifurcation critical value b0. Moreover, stability of the bifurcation periodic solution is analyzed. Secondly, the Turing instability and the direction of Hopf bifurcation of the corresponding to PDE system are investigated by using Normal form theory and Centre manifold theory. Finally, we study the numerical simulations of this system to illustrate the theoretical analysis. |
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| AbstractList | This paper is concerned with a modified Leslie–Gower predator–prey diffusive dynamics system with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is Beddington–DeAngelis (Denote it by B–D) functional response term. Firstly, by applying the theory of stability and the Hopf bifurcation, we discuss the local stability and the existence of the Hopf bifurcation at the positive constant equilibrium solution of the ODE model, which the model undergoes the Hopf bifurcation when bifurcation parameter δ crosses the bifurcation critical value b0. Moreover, stability of the bifurcation periodic solution is analyzed. Secondly, the Turing instability and the direction of Hopf bifurcation of the corresponding to PDE system are investigated by using Normal form theory and Centre manifold theory. Finally, we study the numerical simulations of this system to illustrate the theoretical analysis. |
| ArticleNumber | 113794 |
| Author | Jiang, Yaolin Feng, Xiaozhou Sun, Cong Liu, Xia |
| Author_xml | – sequence: 1 givenname: Xiaozhou surname: Feng fullname: Feng, Xiaozhou email: flxzfxz8@163.com organization: College of Science, Xi’an Technological University, Xi’an 710032, China – sequence: 2 givenname: Xia surname: Liu fullname: Liu, Xia organization: College of Science, Xi’an Technological University, Xi’an 710032, China – sequence: 3 givenname: Cong surname: Sun fullname: Sun, Cong organization: College of Science, Xi’an Technological University, Xi’an 710032, China – sequence: 4 givenname: Yaolin surname: Jiang fullname: Jiang, Yaolin organization: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China |
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| Cites_doi | 10.1016/j.jde.2011.03.004 10.1186/s13662-018-1735-3 10.1007/s12190-013-0663-3 10.1016/j.cnsns.2009.03.006 10.1142/S1793524515500138 10.1016/j.nonrwa.2022.103638 10.1109/ACCESS.2019.2938772 10.1155/2013/267173 10.1016/j.nonrwa.2022.103766 10.1016/j.matcom.2015.05.006 10.1016/j.cnsns.2023.107109 10.1016/j.heliyon.2021.e06193 10.2307/1936298 10.2307/1933011 10.1186/s13662-020-02879-4 10.1016/j.aml.2022.108561 10.1016/j.jmaa.2011.09.049 10.2307/2333294 10.1016/j.matcom.2022.05.017 10.2307/3866 |
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| Keywords | Leslie–Gower model Stability 92D25 Turing instability Neumann boundary condition Hopf bifurcation 35J55 |
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| References | Jiang, Wang, Yao (b16) 2015; 117 Leslie, Gower (b2) 1960; 47 Feng, Sun, Yang, Li (b14) 2023 Ali, Jazar (b6) 2013; 43 Chen, Takeuchi, Zhang (b7) 2023 Li, He, Li (b4) 2022; 201 Feng, Sun, Xiao (b10) 2020; 2020 Jiang, Fang, Wu (b22) 2020; 2020 Sivakumar, Sambath, Balachandran (b25) 2015; 8 Yue, Wang (b19) 2013 Misra, Raveendra (b20) 2014; 2 Fang, Jiang (b1) 2009; 14 Zhang, Wang, Wang (b17) 2011; 387 Feng, Song, Liu, Wang (b9) 2018; 2018 Beddington (b12) 1975; 44 Luo, Wang (b15) 2022 Hassard, Kazarinoff, Wan (b26) 1981 Smith (b18) 1963; 44 Han, Lei (b23) 2022 Ved, Rajnesh, Devendra (b11) 2020; 13 Shi, Cheng, Liu, Li (b21) 2019; 7 Melese, Feyissa (b8) 2021 Wang, Shi, Wei (b24) 2011; 251 Min, Wang (b5) 2018; 23 DeAngelis, Goldstein, O’Neill (b13) 1975; 56 He, Li (b3) 2023 Hassard (10.1016/j.chaos.2023.113794_b26) 1981 Melese (10.1016/j.chaos.2023.113794_b8) 2021 Beddington (10.1016/j.chaos.2023.113794_b12) 1975; 44 Misra (10.1016/j.chaos.2023.113794_b20) 2014; 2 Jiang (10.1016/j.chaos.2023.113794_b22) 2020; 2020 Yue (10.1016/j.chaos.2023.113794_b19) 2013 Ali (10.1016/j.chaos.2023.113794_b6) 2013; 43 Zhang (10.1016/j.chaos.2023.113794_b17) 2011; 387 Ved (10.1016/j.chaos.2023.113794_b11) 2020; 13 Chen (10.1016/j.chaos.2023.113794_b7) 2023 Feng (10.1016/j.chaos.2023.113794_b14) 2023 Smith (10.1016/j.chaos.2023.113794_b18) 1963; 44 Shi (10.1016/j.chaos.2023.113794_b21) 2019; 7 Fang (10.1016/j.chaos.2023.113794_b1) 2009; 14 He (10.1016/j.chaos.2023.113794_b3) 2023 Feng (10.1016/j.chaos.2023.113794_b9) 2018; 2018 Feng (10.1016/j.chaos.2023.113794_b10) 2020; 2020 Wang (10.1016/j.chaos.2023.113794_b24) 2011; 251 Han (10.1016/j.chaos.2023.113794_b23) 2022 Leslie (10.1016/j.chaos.2023.113794_b2) 1960; 47 DeAngelis (10.1016/j.chaos.2023.113794_b13) 1975; 56 Min (10.1016/j.chaos.2023.113794_b5) 2018; 23 Jiang (10.1016/j.chaos.2023.113794_b16) 2015; 117 Li (10.1016/j.chaos.2023.113794_b4) 2022; 201 Sivakumar (10.1016/j.chaos.2023.113794_b25) 2015; 8 Luo (10.1016/j.chaos.2023.113794_b15) 2022 |
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effect of toxicant on a three species food-chain system with food-limited growth of prey population publication-title: Glob J Math Anal – year: 2022 ident: 10.1016/j.chaos.2023.113794_b23 article-title: Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with smith growth function publication-title: Chaos Solitons Fractals – volume: 44 start-page: 331 issue: 1 year: 1975 ident: 10.1016/j.chaos.2023.113794_b12 article-title: Mutual interference between parasites or predators and its effect on searching efficiency publication-title: J Anim Ecol doi: 10.2307/3866 – volume: 2020 start-page: 1 issue: 6 year: 2020 ident: 10.1016/j.chaos.2023.113794_b10 article-title: Stability and coexistence of a diffusive predator-prey system with nonmonotonic functional response and fear effect publication-title: Complexity |
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| Title | Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response |
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