References
- P. N. Brown, Decay to uniform states in ecological interaction, SIAM J. Appl. Math. 38 (1980), no. 1, 22-37. https://doi.org/10.1137/0138002
- Y. H. Fan and L. L. Wang, Global asymptotical stability of a logistic model with feedback control, Nonlinear Anal. Real World Appl. 11 (2010), no. 4, 2686-2697. https://doi.org/10.1016/j.nonrwa.2009.09.016
- T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, J. Differential Equations 244 (2008), no. 5, 1049-1079. https://doi.org/10.1016/j.jde.2007.12.005
- S. Gourley and S. Ruan, Convergence and travelling fronts in functional differential equations with nonlocal term: a competition model, SIAM J. Math. Anal. 35 (2003), no. 3, 806-822. https://doi.org/10.1137/S003614100139991
- H. F. Huo and W. T. Li, Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model, Math. Comput. Modelling 40 (2004), no. 3-4, 261-269. https://doi.org/10.1016/j.mcm.2004.02.026
- Y. Kuang, Delay Differential Equations with Application in Population Dynamics, Academic Press, New York, 1993.
- S. M. Lenhart and C. C. Travis, Global stability of a biological model with time delay, Proc. Amer. Math. Soc. 96 (1986), no. 1, 75-78. https://doi.org/10.1090/S0002-9939-1986-0813814-3
- W. T. Li, G. Lin, and S. Ruan, Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems, Nonlinearity 19 (2006), no. 6, 1253-1273. https://doi.org/10.1088/0951-7715/19/6/003
- Z. Ma, Mathematical Modeling and Research on the Population Ecology, AnHui educational press, Hefei, 1996.
- R. H. Martin and H. L. Smith, Reaction-diffusion systems with time delays: monotonicity, invariance, comparison and convergence, J. Reine Angew. Math. 413 (1991), 1-35.
- C. V. Pao, Convergence of solutions of reaction-diffusion systems with time delays, Nonlinear Anal. 48 (2002), no. 3, Ser. A: Theory Methods, 349-362. https://doi.org/10.1016/S0362-546X(00)00189-9
- R. Peng and M. Wang, Note on a ratio-dependent predator-prey system with diffusion, Nonlinear Anal. Real World Appl. 7 (2006), no. 1, 1-11. https://doi.org/10.1016/j.nonrwa.2004.11.008
- S. Ruan and J.Wu, Reaction-diffusion equations with infinite delay, Canad. Appl. Math. Quart. 2 (1994), no. 4, 485-550.
- S. Ruan and X. Q. Zhao, Persistence and extinction in two species reaction-diffusion systems with delays, J. Differential Equations 156 (1999), no. 1, 71-92. https://doi.org/10.1006/jdeq.1998.3599
- H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr., vol. 41, American Mathematical Society, Providence, RI, 1995.
- Y. Song, M. Han, and Y. Peng, Stability and Hopf bifurcation in a competitive Lotka-Volterra system with two delays, Chaos Solitons Fractals 22 (2004), no. 5, 1139-1148. https://doi.org/10.1016/j.chaos.2004.03.026
- A. M. Turing, The chemical basis of morphogenesis, Philos. Trans. R. Soc. Lond. B 237 (1952), 37-72. https://doi.org/10.1098/rstb.1952.0012
- L. L. Wang and Y. H. Fan, Note on permanence and global stability in delayed ratio-dependent predator-prey models with monotonic functional response, J. Comput. Appl. Math. 234 (2010), no. 2, 477-487. https://doi.org/10.1016/j.cam.2009.12.039
- Y. M. Wang, Asymptotic behavior of solutions for a cooperation-diffusion model with a saturating interaction, Comput. Math. Appl. 52 (2006), no. 3-4, 339-350. https://doi.org/10.1016/j.camwa.2006.03.016
- J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.
- J. Zhen and Z. Ma, Stability for a competitive Lotka-Volterra system with delays, Non-linear Anal. 51 (2002), no. 7, 1131-1142. https://doi.org/10.1016/S0362-546X(01)00881-1