2013

Equilibria in a Dipersal Model for Structured Populations

We derive a model for structured population with a two-phase life cycle. Growth and reproduction occur during the first phase. The first phase is followed by a dispersal phase in which individuals are allowed to move throughout a habitat. Also, we prove the existence of a branch of positive equilibria using bifurcation results of Rabinowitz.

Anahtar Kelimeler:

Integro-difference equations, Dynamical systems, Dispersion, Structured populations

Equilibria in a Dipersal Model for Structured Populations

Keywords:

Integro-difference equations, Dynamical systems, Dispersion, Structured populations,

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Alzoubi, Maref Y. : A dispersal model for structured populations, PhD. Dissertation. The University of Arizona, USA. (1999).
Cohen, D. and Murray, J. D. : A generalized diﬀusion model for growth and dispersal in a population. J. Math. Biol., 12 : 237-249, (1981).
Cushing, J. M. : An introduction to structured population dynamics, SIAM, (1998).
Ellner, S. : Asymptotic behavior of some stochastic diﬀerence equation population models. J. Math. Biol., 19: 169-200, (1984).
Fisher, R. A. : The wave of advance of advantageous genes. Ann. Eugen. London 7: 355-569, (1937).
Hamilton, W. D. and May, R. M. : Dispersal in stable habitats. Nature. 269: 578-581, (1977).
Hardin, D. P., Takak, P. and Webb, G. F. : Asymptotic properties of a continuous-space discrete-time population model in a random environment. Journal of Mathematical Biology. : 361-374, (1988).
Hardin, D. P., Takak, P. and Webb, G. F. : A comparison of a dispersal strategies for survival of spatially heterogenous populations. SIAM Journal on Applied Mathematics. 48: 1423, (1988).
Kolmogrov, A., Petrovsky, I. and Pisconov, N. : Etude de l’equation de las diﬀusion avec croissance de la quatite de matiere et son aplication a un probleme biologique, Moscow Univ. Bull. Ser. Internat. Sect. A. 1: 1-25, (1937).
Kierstead, H. and Slobodkin, L. B. : The size of water masses containing plankton bloom. J. Mar. Res. 12: 141-147, (1953).
Kot, M. and Schaﬀer, W. : Discrete-time growth-dispersal model. Math. Biol.30 : 413-436, (1986).
Krasnoselskii, M. A. : Topological Methods in the Theory of Nonlinear Analysis, Springer Berlin, (1964).
Krasnoselskii, M. A. and Zabreiko, P. P. : Geometrical Methods of Nonlinear Analysis. Spribger, Berlin, (1984).
Cohen, A., Leven, D. and Hastings, A. : Dispersal strategies in patchy environments. Theoret. Population Biol. 26: 165-191, (1984).
Levin, S. A. : Dispersion and population interactions. Amer. Nature. 108 : 207-228, (1974).
Levin, S. A. and Segel, L. A. : Pattern generation in space and aspect. SIAM Rev. 27: 67, (1985).
MacArthur, R. H. and Wilson, E. O. : The Theory of Island Biogeography. Princeton University Press. Princeton. NJ, (1967).
McMurtrie, R. : Persistence and stability of single-species and prey-predator systems in spatially heterogenous environments. Math. Biol. 39: 11-51, (1987).
Okobo, A. : Diﬀusion and ecological problems:Mathematical Models, Biomathematics 10, Springer-Verlag, New York, (1980).
Rabinowitz, P. P. :Some global results for nonlinear eigenvalue problems. Journal of functional analysis 7: 1291-1313, (1971).
Riesz, F. and Nagy: Functional Analysis. Dover, New York, (1990).
Skellam, J. G. : Random dispersal in theoretical populations. Biometrica. 38: 196-218, (1951).
Vance, R. R. : The eﬀect of dispersal on population stability in one-species discrete space population growth model, Amer. Nature. 123: 230-254, (1984).
Van Kirk, R. W. and Lewis, M. A. : Integrodiﬀerence Models For Persistence in Fragmented Habitats. Bullitin of Math. Biol. 59(1): 107-137, (1997).
Zeidler, E. : Nonlinear Functional Analysis and its Applications I. Springer, Berlin, (1992). Maref Y. M. ALZOUBI
Department of Mathematics Yarmouk University Irbid-JORDAN e-mail: maref@yu.edu.jo