Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

WAVEFRONT SOLUTIONS IN THE DIFFUSIVE NICHOLSON'S BLOWFLIES EQUATION WITH NONLOCAL DELAY

  • Zhang, Cun-Hua (Department of Mathematics, Lanzhou Jiaotong University)
  • 발행 : 2010.01.30
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초록

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

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참고문헌

  1. N. Kopell and L. N. Howard, Plane wave solutions to reaction- diffusion equations, Stud. Appl. Math., 52(1973), 291-328.
  2. W. S. C. Gurney, S. P. Blythe, R.M. Nisbet, Nicholsons blowflies revisited, Nature, 287(1980), 17-21. https://doi.org/10.1038/287017a0
  3. R. Law, D. J. Murrell, U. Dieckmann, Population growth in space and time: Spatial logistic equations, Ecology 84(2003), 252-262. https://doi.org/10.1890/0012-9658(2003)084[0252:PGISAT]2.0.CO;2
  4. W. T. Li, S. Ruan, Z. C. Wang, On the Diffusive Nicholsons Blowflies Equation with Nonlocal Delay, J Nonlinear Sci., 17(2007), 505-525. https://doi.org/10.1007/s00332-007-9003-9
  5. G. Lin, Travelling waves in the Nicholsons blowflies equation with spatio-temporal delay, Appl. Math. Comp., 209 (2009), 314-326. https://doi.org/10.1016/j.amc.2008.12.055
  6. A. J. Nicholson, An outline of the dynamics of animal populations, Austral. J. Zoo. 2(1954), 9-65. https://doi.org/10.1071/ZO9540009
  7. H. L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Providence, RI: American Mathematical Society, 1995.
  8. J. W.-H. So and J. Yu, Global attractivity and uniform persistence in Nicholson's blowflies. Diff. Eqns Dynam. Syst., 2(1994), 11-18.
  9. J. W.-H. So, Y. Yang, Dirichlet problem for the diffusive Nicholsons blowflies equation, J. Diff. Equ. 150(1998), 317-348. https://doi.org/10.1006/jdeq.1998.3489
  10. J. W.-H. So, J. Wu, Y. Yang, Numerical Hopf bifurcation analysis on the diffusive Nicholsons blowflies equation, Appl. Math. Comput, 111(2000), 53-69. https://doi.org/10.1016/S0096-3003(99)00047-8
  11. J. W.-H. So, X. Zou, Travelling waves for the diffusive Nicholsons blowflies equation, Appl. Math. Comput. 122(2001), 385-392. https://doi.org/10.1016/S0096-3003(00)00055-2
  12. Z. C. Wang, W. T. Li, S. Ruan, Travelling wave-fronts reaction-diffusion systems with spatio-temporal delays, J. Differ. Equ., 222(2006) 185-232. https://doi.org/10.1016/j.jde.2005.08.010
  13. J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.
  14. Y. Yang, J. W.-H. So, Dynamics for the diffusive Nicholsons blowflies equation. in Dynamical Systems and Differential Equations (ed W. Chen and S. Hu), vol. II, pp. 333-352. Southwest Missouri State University, Springfield (1998)