Spreading speed and travelling wave solutions of a partially sedentary population

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 72, Issue 6, 2007, Pages 801-816

  Volkov, Darko ^a   Lui, Roger ^a  

^a Worcester Polytechnic Institute   (United States)

Author keywords

Monostable; Order preserving; Spreading speed; Travelling wave solutions; Wave speed

Indexed keywords

ASYMPTOTIC ANALYSIS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; POPULATION STATISTICS; PROBABILITY DENSITY FUNCTION;

BEVERTON-HOLT FUNCTION; POPULATION GENETICS MODEL; TRAVELLING WAVE SOLUTIONS;

POPULATION DYNAMICS;

EID: 36549000385     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxm025     Document Type: Article

References (13)

1. ANDOW, D., KAREIVA, P., LEVIN, S. & OKUBO, A. (1990) Spread of invading organisms. Landsc. Ecol., 4, 177-188.
2. ARONSON, D. G. & WEINBERGER, H. (1975) Nonlinear diffusion in population genetics, combustion, and nerve propagation. Partial Differential Equations and Related Topics (J. Goldstein ed.). Lecture Notes in Mathematics, vol. 446. Berlin: Springer, pp. 5-49.
3. BRAZHNIK, P. & TYSON, J. (2000) On traveling wave solutions of Fisher's equation in two spatial dimensions. SIAM J. Appl. Math., 60, 371-391.
4. DIEKMANN, O. & KAPER, H. G. (1978) On the bounded solutions of a nonlinear convolution equation. J. Nonlinear Anal. Theory Method Appl., 3, 355-369.
5. FISHER, R. A. (1937) The advance of advantageous genes. Ann. Eugen., 7, 355-369.
6. INTERGOVERNMENTAL PANEL ON CLIMATE CHANGE (IPCC) (2007). Climate change 2007: Impacts, adaptation and vulnerability. Working Group II Contribution to the Intergovernmental Panel on Climate Change Fourth Assessment Report. Available at http://www.ipcc-wg2.org/.
7. KOT, M., LEWIS, M. A. & VAN DEN DRIESSCHE, P. (1996) Dispersal data and the spread of invading organisms. Ecology, 77, 2027-2042.
8. LUBINA, J. A. & LEVIN, S. A. (1988) The spread of a reinvading species: Range expansion in the California sea otter. Am. Nat., 131, 526-543.
9. LUI, R. (1982) A nonlinear integral operator arising from a model in population genetics, I. Monotone initial data. SIAM J. Math. Anal. 13, 913-937.
10. SKELLAM, J. G. (1951) Random dispersal in theoretical populations. Biometrika, 38, 196-218.
11. VEIT, R. R. & LEWIS, M. A. (1996) Dispersal, population growth, and the Allee effect: Dynamics of the House Finch invasion of eastern North America. Am. Nat., 148, 255-274.
12. WEINBERGER, H. (1978) Asymptotic behavior of a model in population genetics. Nonlinear Partial Differential Equations and Applications (J. Chadam ed.). Lecture Notes in Mathematics, vol. 648. New York: Springer, pp. 47-98.
13. WEINBERGER, H. (1982) Long time behavior of a class of biological models. SIAM J. Math. Anal., 13, 353-396.