Dynamics of a predator–prey model with nonlinear growth rate and B–D functional response
In this paper, a predator–prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington–DeAngelis functional response and nonlinear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the...
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| Published in | Nonlinear analysis: real world applications Vol. 70; p. 103766 |
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| Format | Journal Article |
| Language | English |
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01.04.2023
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| Abstract | In this paper, a predator–prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington–DeAngelis functional response and nonlinear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the main parameter, we mainly investigate the existence, stability and exact number of positive solutions when m is large and other parameters meet a certain range of conditions. Meanwhile, some numerical simulations are applied to illustrate the analytical results. The main techniques used in this paper include the fixed point index theory, the super-sub solution method, the Lyapunov-Schmidt reduction procedure and the perturbation principle. |
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| AbstractList | In this paper, a predator–prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington–DeAngelis functional response and nonlinear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the main parameter, we mainly investigate the existence, stability and exact number of positive solutions when m is large and other parameters meet a certain range of conditions. Meanwhile, some numerical simulations are applied to illustrate the analytical results. The main techniques used in this paper include the fixed point index theory, the super-sub solution method, the Lyapunov-Schmidt reduction procedure and the perturbation principle. |
| ArticleNumber | 103766 |
| Author | Yang, Wenbin Feng, Xiaozhou Sun, Cong Li, Changtong |
| Author_xml | – sequence: 1 givenname: Xiaozhou orcidid: 0000-0001-9349-1432 surname: Feng fullname: Feng, Xiaozhou email: flxzfxz8@163.com organization: School of Science, Xi’an Technological University, Xi’an 710032, China – sequence: 2 givenname: Cong surname: Sun fullname: Sun, Cong organization: School of Science, Xi’an Technological University, Xi’an 710032, China – sequence: 3 givenname: Wenbin surname: Yang fullname: Yang, Wenbin organization: School of Science, Xi’an University of post and Telecommunications, Xi’an 710121, China – sequence: 4 givenname: Changtong surname: Li fullname: Li, Changtong organization: School of Science, Xi’an Technological University, Xi’an 710032, China |
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| Cites_doi | 10.1002/cpa.3160471203 10.57262/die/1369330437 10.1090/S0002-9947-97-01842-4 10.1137/0517094 10.1016/j.amc.2009.09.003 10.1080/00036819108840010 10.1016/S0362-546X(98)00250-8 10.1016/j.na.2006.02.049 10.2307/3866 10.1016/j.nonrwa.2007.08.020 10.1016/j.apm.2007.09.007 10.2307/1936298 10.1006/jmaa.2000.7343 10.1016/j.jde.2011.04.017 10.1016/j.nonrwa.2015.07.010 10.2307/1087 10.1016/j.nonrwa.2018.07.012 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2 10.1016/S0022-247X(02)00395-5 |
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| References | DeAngelis, Goldstein, O’Neill (b9) 1975; 56 Gause (b1) 1936 Pao (b17) 1992 Cantrell, Cosner (b6) 2001; 257 Smoller (b27) 1994 Blat, Brown (b20) 1986; 17 Wang (b26) 1993 Casal, Eilbeck, Lopez-Gomez (b18) 1994; 7 Laurin, Rousseau (b5) 2011; 251 Beddington (b8) 1975; 44 Schaefer, Wolff (b14) 1999 Wu (b28) 2000; 39 Yamada (b15) 2008 Beverton, Holt (b10) 1956 De la Sen (b12) 2008; 32 Li, Ghoreishi (b23) 1991; 40 Hwang (b7) 2002; 281 Li, Li, Yang (b21) 2016; 27 Skalski, Gilliam (b4) 2001; 82 Nie, Wu (b25) 2009; 10 Tang, Cheke, Xiao (b11) 2006; 65 Wang (b16) 2010 Gui, Lou (b19) 1994; 47 Gause, Smaragdova, Witt (b2) 1936; 5 Meng, Yang (b22) 2019; 45 Ruan, Xiao (b3) 2000; 61 De la Sen, Alonso-Quesada (b13) 2009; 215 Du, Lou (b24) 1997; 349 Du (10.1016/j.nonrwa.2022.103766_b24) 1997; 349 Casal (10.1016/j.nonrwa.2022.103766_b18) 1994; 7 Skalski (10.1016/j.nonrwa.2022.103766_b4) 2001; 82 Beddington (10.1016/j.nonrwa.2022.103766_b8) 1975; 44 Nie (10.1016/j.nonrwa.2022.103766_b25) 2009; 10 De la Sen (10.1016/j.nonrwa.2022.103766_b12) 2008; 32 Wang (10.1016/j.nonrwa.2022.103766_b16) 2010 Gui (10.1016/j.nonrwa.2022.103766_b19) 1994; 47 Wu (10.1016/j.nonrwa.2022.103766_b28) 2000; 39 Gause (10.1016/j.nonrwa.2022.103766_b2) 1936; 5 Beverton (10.1016/j.nonrwa.2022.103766_b10) 1956 Gause (10.1016/j.nonrwa.2022.103766_b1) 1936 Laurin (10.1016/j.nonrwa.2022.103766_b5) 2011; 251 Yamada (10.1016/j.nonrwa.2022.103766_b15) 2008 Li (10.1016/j.nonrwa.2022.103766_b21) 2016; 27 Cantrell (10.1016/j.nonrwa.2022.103766_b6) 2001; 257 Schaefer (10.1016/j.nonrwa.2022.103766_b14) 1999 Li (10.1016/j.nonrwa.2022.103766_b23) 1991; 40 Ruan (10.1016/j.nonrwa.2022.103766_b3) 2000; 61 De la Sen (10.1016/j.nonrwa.2022.103766_b13) 2009; 215 Wang (10.1016/j.nonrwa.2022.103766_b26) 1993 Tang (10.1016/j.nonrwa.2022.103766_b11) 2006; 65 Smoller (10.1016/j.nonrwa.2022.103766_b27) 1994 Pao (10.1016/j.nonrwa.2022.103766_b17) 1992 DeAngelis (10.1016/j.nonrwa.2022.103766_b9) 1975; 56 Blat (10.1016/j.nonrwa.2022.103766_b20) 1986; 17 Meng (10.1016/j.nonrwa.2022.103766_b22) 2019; 45 Hwang (10.1016/j.nonrwa.2022.103766_b7) 2002; 281 |
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| Title | Dynamics of a predator–prey model with nonlinear growth rate and B–D functional response |
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