Monotone travelling fronts of a food-limited population model with nonlocal delay. (English) Zbl 1152.35408

Summary: This paper deals with the existence of monotone travelling fronts of a diffusive food-limited population model with nonlocal delay. By choosing different kernel functions, we establish some existence criteria of monotone travelling fronts connecting two uniform steady states of the model, which include, improve and/or complement a number of existing results.


35K57 Reaction-diffusion equations
35B20 Perturbations in context of PDEs
92D25 Population dynamics (general)
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[1] Ashwin, P. B.; Bartuccelli, M. V.; Bridges, T. J.; Gourley, S. A., Travelling fronts for the KPP equation with spatio-temporal delay, Z. Angew. Math. Phys., 53, 103-122 (2002) · Zbl 1005.92024
[2] Canosa, J., On a nonlinear diffusion equation describing population growth, IBM J. Res. Dev., 17, 307-386 (1973) · Zbl 0266.65080
[3] Feng, W.; Lu, X., On diffusive population models with toxicants and time delays, J. Math. Anal. Appl., 233, 373-386 (1999) · Zbl 0927.35049
[4] Feng, W.; Lu, X., Global periodicity in a class of reaction-diffusion systems with time delays, Discrete Cont. Dyn. Syst., 3B, 69-78 (2003) · Zbl 1078.35126
[5] Fenichel, N., Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations, 31, 53-98 (1979) · Zbl 0476.34034
[6] Gopalsamy, K.; Kulenovic, M. R.S.; Ladas, G., Time lags in a “food-limited” population model, Appl. Anal., 31, 225-237 (1988) · Zbl 0639.34070
[7] Gopalsamy, K.; Kulenovic, M. R.S.; Ladas, G., Environmental periodicity and time delays in a “food-limited” population model, J. Math. Anal. Appl., 147, 545-555 (1990) · Zbl 0701.92021
[8] Gourley, S. A., Travelling front solutions of a nonlocal Fisher equation, J. Math. Biol., 41, 272-284 (2000) · Zbl 0982.92028
[9] Gourley, S. A., Wave front solutions of a diffusive delay model for populations of Daphnia magna, Comput. Math. Appl., 42, 1421-1430 (2001) · Zbl 0998.92029
[10] Gourley, S. A.; Chaplain, M. A.J., Travelling fronts in a food-limited population model with time delay, Proc. R. Soc. Edinburgh Sect. A, 132, 75-89 (2002) · Zbl 1006.35051
[11] Gourley, S. A.; Ruan, S., Convergence and travelling fronts in functional differential equations with nonlocal terms: a competition model, SIAM J. Math. Anal., 35, 806-822 (2003) · Zbl 1040.92045
[12] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press: Academic Press New York · Zbl 0777.34002
[13] Pielou, E. C., An Introduction to Mathematical Ecology (1969), Wiley: Wiley New York · Zbl 0259.92001
[14] Smith, F. E., Population dynamics in Daphnia magna, Ecology, 44, 651-663 (1963)
[15] So, J. W.-H.; Yu, J. S., On the uniform stability for a “food-limited” population model with time delay, Proc. R. Soc. Edinburgh Sect. A, 125, 991-1005 (1995) · Zbl 0844.34079
[16] Song, Y.; Peng, Y.; Han, M., Travelling wavefronts in the diffusive single species model with Allee effect and distributed delay, Appl. Math. Comput., 152, 483-497 (2004) · Zbl 1041.92027
[17] Wang, Z. C.; Li, W. T.; Ruan, S., Travelling wave fronts of reaction-diffusion systems with spatio-temporal delays, J. Differential Equations, 222, 185-232 (2006) · Zbl 1100.35050
[18] Wu, J.; Zou, X., Travelling wave fronts of reaction-diffusion systems with delay, J. Dyn. Differential Equations, 13, 651-687 (2001) · Zbl 0996.34053
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