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