Dynamics for a Three-Species Predator-Prey Model with Density-Dependent Motilities
Tóm tắt
Từ khóa
Tài liệu tham khảo
Alikakos, N.D.: $$L^p$$ bounds of solutions of reaction-diffusion equations. Comm. Partial Diff. Equ. 4, 827–868 (1979)
Amann, H.: Dynamic theory of quasilinear parabolic equations III. Global existence. Math. Z. 202, 219–250 (1989)
Amann, H.: Dynamic theory of quasilinear parabolic equations II. Reaction-diffusion systems. Diff. Integr. Equ. 3, 13–75 (1990)
Amann, H.: Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), volume 133 of Teubner-Texte Math., pages 9-126. Teubner, Stuttgart (1993)
Bai, X., Winkler, M.: Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Indiana Univ. Math. J. 65, 553–583 (2016)
Chakraborty, A., Singh, M., Lucy, D., Ridland, P.: Predator-prey model with preytaxis and diffusion. Math. Comput. Model. 46, 482–498 (2007)
Ainseba, B.E., Bendahmane, M., Noussair, A.: A reaction-diffusion system modeling predator-prey with prey-taxis. Nonlinear Anal. Real World Appl. 9, 2086–2105 (2008)
Lee, J.M., Hilllen, T., Lewis, M.A.: Continuous traveling waves for prey-taxis. Bull. Math. Biol. 70, 654–676 (2008)
Lee, J.M., Hilllen, T., Lewis, M.A.: Pattern formation in prey-taxis systems. J. Biol. Dyn. 3, 551–573 (2009)
Li, C., Wang, X., Shao, Y.: Steady states of a predator-prey model with prey-taxis. Nonlinear Anal. 97, 155–168 (2014)
He, X., Zheng, S.: Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis. Appl. Math. Lett. 49, 73–77 (2015)
Hirata, M., Kurima, S., Mizukami, M., Yokota, T.: Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics. J. Diff. Equ. 263, 470–490 (2017)
Holling, C.: The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entom. Soc. Can. 45, 1–60 (1965)
Hsiao, L., De Mottoni, P.: Persistence in reacting-diffusing systems: Interaction of two predators and one prey. Nonlinear Anal. 11, 877–891 (1987)
Jin, H., Kim, Y., Wang, Z.A.: Boundedness, stabilization, and pattern formation driven by densitysuppressed motility. SIAM J. Appl. Math. 78, 1632–1657 (2018)
Jin, H., Wang, Z.: Global dynamics and spatio-temporal patterns of predator-prey systems with density-dependent motion. Eur. J. Appl. Math. (2021). https://doi.org/10.1017/S0956792520000248
Kareiva, P., Odell, G.T.: Swarms of predators exhibit “preytaxis’ if individual predators use area-restricted search. Am. Nat. 130, 233–270 (1987)
Lankeit, J., Wang, Y.: Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption. Discret. Contin. Dyn. Syst. 37, 6099–6121 (2017)
Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins Co., Baltimore (1925)
Lin, J., Wang, W., Zhao, C., Yang, T.: Global dynamics and traveling wave solutions of two predators-one prey models. Discret. Contin. Dyn. Syst. Ser. B 20, 1135–1154 (2015)
Loladze, I., Kuang, Y., Elser, J.J., Fagan, W.F.: Competition and stoichiometry: coexistence of two predators on one prey. Theo. Popul. Biol. 65, 1–15 (2004)
Pang, P., Wang, M.: Strategy and stationary pattern in a three-species predator-prey model. J. Diff. Equ. 200, 245–273 (2004)
Porzio, M., Vespri, V.: H$$\ddot{o}$$lder estimates for local solutions of some doubly nonlinear degenerate parabolic equations. J. Diff. Equ. 103, 146–178 (1993)
Tao, Y.: Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis. Nonlinear Anal. Real World Appl. 11, 2056–2064 (2010)
Tello, J.I., Wrzosek, D.: Predator-prey model with diffusion and indirect prey-taxis. Math. Model. Method. Appl. Sci. 26, 2129–62 (2016)
Tona, T., Hieu, N.: Dynamics of species in a model with two predators and one prey. Nonlinear Anal. 74, 4868–4881 (2011)
Volterra, V.: Fluctuations in the abundance of a species considered mathematically. Nature 118, 558–560 (1926)
Wang, J., Wang, M.: Boundeness and global stability of the two-predator and one-prey models with nonlinear prey-taxis. Z. Angew. Math. Phys. 69, 63 (2018)
Wang, J., Wang, M.: The diffusive Beddington-DeAngelis predator-prey model with nonlinear prey-taxis and free boundary. Math. Method. Appl. Sci. 41, 6741–6762 (2018)
Wang, J., Wang, M.: Global solution of a diffusive predator-prey model with prey-taxis. Comput. Math. Appl. 77, 2676–94 (2019)
Wang, J., Wang, M.: The dynamics of a predator-prey model with diffusion and indirect prey-taxis. J. Dyn. Differ. Equ. (2019). https://doi.org/10.1007/s10884-019-09778-7
Wang, K., Wang, Q., Yu, F.: Stationary and time-periodic patterns of two-predator and one-prey systems with prey-taxis. Discret. Contin. Dyn. Syst. 37(1), 505–543 (2017)
Wang, Q., Gai, C., Yan, J.: Qualitative analysis of a Lotka-Volterra competition system with advection. Discret. Contin. Dyn. Syst. 35, 1239–1284 (2015)
Wang, Q., Song, Y., Shao, L.: Nonconstant positive steady states and pattern formation of 1D prey-taxis systems. J. Nonlinear Sci. 1–27,(2016)
Wang, X., Wang, W., Zhang, G.: Global bifurcation of solutions for a predator-prey model with prey-taxis. Math. Method. Appl. Sci. 38, 431–443 (2015)
Wang, Z.A., Xu, J.: On the Lotka-Volterra competition system with dynamical resources and density-dependent diffusion. J. Math. Biol. (2021). https://doi.org/10.1007/s00285-021-01562-w
Winkler, M.: Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. J. Diff. Equ. 263, 4826–69 (2017)
Wu, S., Shi, J., Wu, B.: Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis. J. Diff. Equ. 260, 5847–74 (2016)