Wavefront Solutions in the Diffusive Nicholson’s Blowflies Equation With Nonlocal Delay

ZHANG Cun-hua; YAN Xiang-ping

doi:10.3879/j.issn.1000-0887.2010.03.011

Volume 31 Issue 3

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ZHANG Cun-hua, YAN Xiang-ping. Wavefront Solutions in the Diffusive Nicholson’s Blowflies Equation With Nonlocal Delay[J]. Applied Mathematics and Mechanics, 2010, 31(3): 360-368. doi: 10.3879/j.issn.1000-0887.2010.03.011

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Wavefront Solutions in the Diffusive Nicholson’s Blowflies Equation With Nonlocal Delay

doi: 10.3879/j.issn.1000-0887.2010.03.011

Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, P. R. China

Received Date: 1900-01-01
Rev Recd Date: 2009-12-16
Publish Date: 2010-03-15

Abstract

Abstract

The diffusive Nicholson.s blow flies equation with a nonlocal delay in corporated as an integral convolution over all the past tmie up to now and the whole one-dmiensional spatial doma in was studied. When the delay kernel is assumed to be the strong generic kernel, by using the linear chain te chniques and the geometric singularperturbation theory, the existence of trave lling front solutions is shown for small delay.
- diffusive Nicholson’s blow flies equation,
- nonlocal delay,
- strong generic kernel,
- travelling wave front solution

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References(15)

References

[1]	Nicholson A J. An outline of the dynamics of animal populations[J]. Aust J Zool, 1954, 2(1): 9-65.
[2]	Gurney W S C, Blythe S P, Nisbet R M. Nicholson’s blowflies revisited[J]. Nature, 1980, 287: 17-21. doi: 10.1038/287017a0
[3]	Kopell N, Howard L N. Plane wave solutions to reaction-diffusion equations[J]. Stud Appl Math,1973，52: 291-328.
[4]	Smith H L.Monotone Dynamical Systems: an Introduction to the Theory of Competitive and Cooperative Systems[M]. Providence RI：American Mathematical Society, 1995.
[5]	So J W-H, Yu J S. Global attractivity and uniform persistence in Nicholson’s blowflies[J]. Diff Equ Dyn Sys, 1994,2(1): 11-18.
[6]	Law R, Murrell D J, Dieckmann U. Population growth in space and time: spatial logistic equations[J]. Ecology, 2003，84(1): 252-262.
[7]	Yang Y, So J W-H. Dynamics for the diffusive Nicholson’s blowflies equation[C]Chen W, Hu S.Dynamical Systems and Differential Equations. Vol II. Springfield：Southwest Missouri State University, 1998： 333-352.
[8]	So J W-H, Wu J, Yang Y. Numerical Hopf bifurcation analysis on the diffusive Nicholson’s blowflies equation[J]. Appl Math Comput, 2000, 111(1): 53-69.
[9]	So J W-H, Zou X. Travelling waves for the diffusive Nicholson’s blowflies equation[J]. Appl Math Comput, 2001, 122(1): 385-392. doi: 10.1016/S0096-3003(00)00055-2
[10]	So J W-H, Yang Y. Dirichlet problem for the diffusive Nicholson’s blowflies equation[J]. J Differential Equations, 1998, 150(1): 317-348.
[11]	张建明，彭亚红. 具有非局部反应的时滞扩散Nicholson方程的行波解[J]. 数学年刊，A辑， 2006, 27(6): 771-778.
[12]	Li W T, Ruan S， Wang Z C. On the diffusive Nicholson’s blowflies equation with nonlocal delay[J]. J Nonlinear Sci, 2007, 17(6): 505-525.
[13]	Lin G. Travelling waves in the Nicholson’s blowflies equation with spatio-temporal delay[J]. Appl Math Comp, 2009, 209(2): 314-332. doi: 10.1016/j.amc.2008.12.055
[14]	Wang Z C, Li W T, Ruan S. Travelling wave-fronts in reaction-diffusion systems with spatio-temporal delays[J]. J Differential Equations, 2006, 222(1): 185-232.
[15]	Fenichel N. Geometric singular perturbation theory for ordinary diferential equations[J]. J Differential Equations, 1979, 31(1): 53-98. doi: 10.1016/0022-0396(79)90152-9