Local bifurcation of a Ronsenzwing-MacArthur predator prey model with two prey-taxis

Xue Xu; Yibo Wang; Yuwen Wang

doi:10.3934/mbe.2019086

Mathematical Biosciences and Engineering, 2019, 16(4): 1786-1797. doi: 10.3934/mbe.2019086. Research article Special Issues

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Local bifurcation of a Ronsenzwing-MacArthur predator prey model with two prey-taxis

Xue Xu, Yibo Wang, Yuwen Wang

1 Department of Mathematics, Harbin University, Harbin, Heilongjiang, 150001, P.R. China
2 Institute of Telecommunication Satellite, China Academy of Space Technology, P.R. China
3 School of Mathematical and Science, Harbin Normal University, Harbin, Heilongjiang, 150025, P.R. China

Received: , Accepted: , Published:

Special Issues: Differential Equations in Mathematical Biology

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The paper investigates the steady state bifurcation analysis in a general Ronsenzwing-MacArthur predator prey model with two prey-taxis under Neumann boundary conditions. The results show that the rich dynamics in predator prey systems with two prey taxis.

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Keywords: predator-prey; taxis; steady state; bifurcation; Neumann boundary

Citation: Xue Xu, Yibo Wang, Yuwen Wang. Local bifurcation of a Ronsenzwing-MacArthur predator prey model with two prey-taxis. Mathematical Biosciences and Engineering, 2019, 16(4): 1786-1797. doi: 10.3934/mbe.2019086

References:

1. B. Ainseba, M. Bendahmane and A. Noussair, A reaction-diffusion system modeling predator-prey with prey-taxis, Nonl. Anal.: Real World Applications, 9 (2008) 5, 2086–2105.
2. H. Amann, Dynamic theory of quasilinear parabolic equations II, Reaction-diffusion systems, Diff. Int. Eqns., 3 (1990), 13–75.
3. M. Bendahmane, Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis, Network and Heterogeneous Media, 3 (2008), 863–879.
4. L. L. Chen and G. H. Zhang, Global existence of classical solutions to a three-species predatorprey model with two prey-taxis, J. Appl. Math., 10(2012), 1155–1167.
5. A. K. Drangeid, The principle of linearized stability for quasilinear parabolic evolution equations, Nonlinear Analysis, 13 (1989), 1091–1113.
6. H. Y. Jin and Z. A. Wang. Global stability of prey-taxis systems, J. Diff. Eqns., 3(2017), 1257– 1290.
7. E. F. Keller and L. A. Segel. Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol., 26(3) (1970) 399–415.
8. P. Liu, J. P. Shi and Z. A. Wang, Pattern formation of attraction-repulsion Keller-Segel system, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 2597–2625.
9. D. M. Liu and Y. S. Tao, Global boundedness in a fully parabolic attraction-repulsion chemotaxis model, Math. Methods Appl. Sci., 38 (2015), 2537–2546.
10. G. Simonett, Center manifolds for quasilinear reaction-diffusion systems, Diff. Integr. Eqns., 8 (1995), 753–796.
11. J. P. Shi and X. F. Wang, On global bifurcation for quasilinear elliptic systems on bounded domains, J. Diff. Eqns., 246 (2009), 2788–2812.
12. Y. Tao, Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis, Nonl. Anal.: Real World Applications, 11 (2010), 2056–2064.
13. Y. S. Tao. Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 2705–2722.
14. J. F. Wang, J. P. Shi and J. J. Wei, Dynamics and pattern formation in a diffusion predator-prey system with strong Allee effect in prey, J. Diff. Eqns., 251 (2011), 1276–1304.
15. X. F. Wang and Q. Xu, Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness, J. Math. Biol., 66 (2013), 1241–1266.
16. X. L. Wang, W. D. Wang and G. H. Zhang, Global bifurcation of solutions for a predator-prey model with prey-taxis, Math. Meth. Appl. Sci., 3 (2014), 431–443.
17. M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Diff. Eqns., 248 (2010) (12), 2889–2905.
18. S. N. Wu, J. P. Shi, and B. Y. Wu. Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis, J. Diff. Eqns., 260 (2016), 5847–5874.

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