Global dynamics of a Lotka-Volterra type prey–predator model with diffusion and predator-taxis

References

• Cantrell RS, Cosner C. Spatial ecology via reaction-diffusion equations. Series in Mathematical and Computational Biology. Chichester, UK; John Wiley and Sons; 2003.
   Google Scholar
• Murray JD. Mathematical biology I: an introduction, NewYork: Springer-Verlag :volume I. 2003.
   Google Scholar
• Rosenzweig ML. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Sci. 1971;171(3969):385–387.
   PubMed Web of Science ®Google Scholar
• Wang J, Shi J, Wei J. Predator–prey system with strong Allee effect in prey. J Math Biol. 2011;62(3):291–331.
   PubMed Web of Science ®Google Scholar
• Biktashev VN, Tsyganov MA. Pursuit-evasion predator-prey waves in two spatial dimensions. Chaos: Interdiscipl J Nonlin Sci. 2004;14(4):988–994.
   PubMed Web of Science ®Google Scholar
• Lee S-H, Park JH, Chon T-S, Pak HK. Prey-flock deformation under a predator's attack. J Korean Phys Soc. 2006;48:S236.
   Web of Science ®Google Scholar
• MacKenzie BR, Kiørboe T. Encounter rates and swimming behavior of pause-travel and cruise larval fish predators in calm and turbulent laboratory environments. Limnol Oceanogr. 1995;40(7):1278–1289.
   Web of Science ®Google Scholar
• Parrish JK, Viscido SV, Grunbaum D. Self-organized fish schools: an examination of emergent properties. Biol Bull. 2002;202(3):296–305.
   PubMed Web of Science ®Google Scholar
• Ainseba B, Bendahmane M, Noussair A. A reaction–diffusion system modeling predator–prey with prey-taxis. Nonlinear Anal: Real World Appl. 2008;9(5):2086–2105.
   Web of Science ®Google Scholar
• Kareiva P, Odell G. Swarms of predators exhibit “preytaxis” if individual predators use area-restricted search. Am Nat. 1987;130(2):233–270.
   Web of Science ®Google Scholar
• Lee JM, Hillen T, Lewis MA. Pattern formation in prey-taxis systems. J Biol Dyn. 2009;3(6):551–573.
   PubMedGoogle Scholar
• Ahn I, Yoon C. Global well-posedness and stability analysis of prey-predator model with indirect prey-taxis. J Differ Equ. 2020;268(8):4222–4255.
   Web of Science ®Google Scholar
• Cai Y, Cao Q, Wang ZA. Asymptotic dynamics and spatial patterns of a ratio-dependent predator–prey system with prey-taxis. Appl Anal. 2020;1–19.
   Web of Science ®Google Scholar
• He X, Zheng S. Global boundedness of solutions in a reaction–diffusion system of predator–prey model with prey-taxis. Appl Math Lett. 2015;49:73–77.
   Web of Science ®Google Scholar
• Jin HY, Wang ZA. Global stability of prey-taxis systems. J Differ Equ. 2017;262(3):1257–1290.
   Web of Science ®Google Scholar
• Jin HY, Wang ZA. Global dynamics and spatio-temporal patterns of predator-prey systems with density-dependent motion. 2019. arXiv preprint arXiv:1907.02312.
   Google Scholar
• Tao Y. Global existence of classical solutions to a predator–prey model with nonlinear prey-taxis. Nonlinear Anal: Real World Appl. 2010;11(3):2056–2064.
   Web of Science ®Google Scholar
• Wang Q, Song Y, Shao L. Nonconstant positive steady states and pattern formation of 1D prey-taxis systems. J Nonlinear Sci. 2017;27(1):71–97.
   Web of Science ®Google Scholar
• Wu S, Shi J, Wu B. Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis. J Differ Equ. 2016;260(7):5847–5874.
   Web of Science ®Google Scholar
• Xiang T. Global dynamics for a diffusive predator–prey model with prey-taxis and classical Lotka–Volterra kinetics. Nonlinear Anal: Real World Appl2018;39:278–299.
   Web of Science ®Google Scholar
• Wu S, Wang J, Shi J. Dynamics and pattern formation of a diffusive predator–prey model with predator-taxis. Math Models Methods Appl Sci. 2018;28(11):2275–2312.
   Web of Science ®Google Scholar
• Ahn I, Yoon C. Global solvability of prey–predator models with indirect predator-taxis. Z Für Angewandte Mathematik Phys. 2021;72(1):1–20.
   Web of Science ®Google Scholar
• Amann H. Dynamic theory of quasilinear parabolic equations. II. reaction-diffusion systems. Differ Integral Equ. 1990;3(1):13–75.
   Google Scholar
• Amann H. Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. Funct Spaces Differ Oper Nonlinear Anal. 1993;133: 9–126.
   Google Scholar
• Tao Y, Winkler M. Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system. Z Für Angewandte Mathematik Phys. 2016;67(6):138.
   Web of Science ®Google Scholar
• LaSalle J. Some extensions of Liapunov's second method. IRE Trans Circuit Theory. 1960;7(4):520–527.
   Google Scholar
• Porzio MM, Vespri V. Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations. J Differ Equ. 1993;103(1):146–178.
   Web of Science ®Google Scholar
• Ladyzhenskaia OA, Solonnikov VA, Ural'ceva NN. Linear and quasi-linear equations of parabolic type. American Mathematical Soc. 1968.
   Google Scholar
• Tao Y, Winkler M. Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. SIAM J Math Anal. 2015;47(6):4229–4250.
   Web of Science ®Google Scholar