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Analysis of nonautonomous predator-prey model with nonlinear diffusion and time delay. (English) Zbl 1147.34355
This paper deals with the uniform persistence and global stability of a nonautonomous predator-prey model with nonlinear diffusion and delay effect. The main technique is based on the construction of a suitable Lyapunov functional.

MSC:
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
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[1] Levin, S.A., Dispersion and population interaction, Am. nat., 108, 207-228, (1994)
[2] Allen, L.J.S., Persistence and extinction in single-species reaction-diffusion models, Bull. math. biol., 45, 2, 209-227, (1983) · Zbl 0543.92020
[3] Song, X.Y.; Chen, L.S., Uniform persistence and global attractivity for nonautonomous competitive systems with dispersion, J. syst. sci. complex., 15, 307-314, (2002) · Zbl 1027.92027
[4] A Cui, J.; Chen, L.S., Permanence and extinction in logistic and lotka – volterra system with diffusion, J. math. anal. appl., 258, 2, 512-535, (2001) · Zbl 0985.34061
[5] Beretta, E.; Takeuchi, Y., Global asymptotic stability of lotka – volterra diffusion models with continuous time delays, SIAM J. appl. math., 48, 627-651, (1988) · Zbl 0661.92018
[6] Beretta, E.; Solimano, F., Global stability and periodic orbits for two patch predator-prey diffusion delay models, Math. biosci., 85, 153-183, (1987) · Zbl 0634.92017
[7] Butler, G.J.; Freedman, H.; Waltman, P., Uniformly persistent systems, Proc. am. math. soc., 96, 425-429, (1986) · Zbl 0603.34043
[8] Freedman, H.; Waltman, P., Persistence in models of three interacting predator-prey populations, Math. biosci., 68, 213-231, (1984) · Zbl 0534.92026
[9] Freedman, H.; Waltman, P., Persistence in a model of three competitive populations, Math. biosci., 73, 89-101, (1985) · Zbl 0584.92018
[10] Song, X.Y.; Chen, L.S., Optimal harvesting and stability with stage-structure for a two species competitive system, Math. biosci., 170, 173-186, (2001) · Zbl 1028.34049
[11] Gopalsamy, K., Stability and oscillation in delay differential equations of population dynamics, (1992), kluwer Acaderemic Publishers Natherlands Dordrecht · Zbl 0752.34039
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