Traveling wave fronts in a delayed population model of Daphnia magna

This paper deals with the traveling wave fronts of a delayed population model with nonlocal dispersal. By constructing proper upper and lower solutions, the existence of the traveling wave fronts is proved. In particular, we show such a traveling wave front is strictly monotone.

[1]  Paul C. Fife,et al.  Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions , 2003 .

[2]  Mustafa R. S. Kulenovic,et al.  Environmental periodicity and time delays in a “food-limited” population model , 1990 .

[3]  Mustafa R. S. Kulenovic,et al.  Time lags in a “food–limited” population , 1988 .

[4]  Shuxia Pan,et al.  Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity , 2008 .

[5]  Xin Lu,et al.  Global periodicity in a class of reaction-diffusion systems with time delays , 2002 .

[6]  Jérôme Coville,et al.  On a non-local equation arising in population dynamics , 2007, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[7]  Frederick E. Smith,et al.  Population Dynamics in Daphnia magna and a New Model for Population Growth , 1963 .

[8]  Jianhua Huang,et al.  Existence of traveling wave fronts of delayed lattice differential equations , 2004 .

[9]  P. Bates,et al.  Traveling Waves in a Convolution Model for Phase Transitions , 1997 .

[10]  Jack Carr,et al.  Uniqueness of travelling waves for nonlocal monostable equations , 2004 .

[11]  E. C. Pielou.  An introduction to mathematical ecology , 1970 .

[12]  Wan-Tong Li,et al.  Monotone travelling fronts of a food-limited population model with nonlocal delay , 2007 .

[13]  Xin Lu,et al.  On Diffusive Population Models with Toxicants and Time Delays , 1999 .

[14]  Joseph W.-H. So,et al.  On the uniform stability for a ‘food-limited’ population model with time delay , 1995, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[15]  Rolf Rannacher,et al.  Trends in Nonlinear Analysis , 2002 .

[16]  S. A. Gourley.  Wave front solutions of a diffusive delay model for populations of Daphnia magna , 2001 .

[17]  Mark A. J. Chaplain,et al.  Travelling fronts in a food-limited population model with time delay , 2002, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.