大小结构种群模型的平衡解的稳定性

Abstract

Abstract:

In this paper, the authors are concerned with a nonlinear size-structured population model with the vital rates depending both on the individuals' size and on the total population. They arrive at a characteristic equation by the
perturbation method and analyze the stability of equilibrium solutions. For some special cases, sufficient conditions for the stability of equilibrium solutions are obtained.

Key words: Stability, Equilibrium solution, Size-structured population model

CLC Number:

92D25

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LIU Ke-Ying, LIU Wei-An. Stability of Equilibrium Solutions to Size-structured Population Models[J].Acta mathematica scientia,Series A, 2010, 30(2): 417-424.

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References

[1] Ackleh A S, Banks H T, Deng K. A finite difference approximation for a coupled system of nonlinear size-structured populations. Nonliner Anal, 2002, 50: 727--748

[2] Ackleh A S, Deng K. Monotone method for first order nonlocal hyperbolic initial boundary value problems. Appl Anal, 1997, 67: 283--293

[3] Calsina Á, Saldana J. A model of physiologically structured population dynamics with a nonlinear individual growth rate. J Math Biol, 1995, 33: 335--364

[4] Calsina Á. Global dynamics and optimal life history of a structured population model. SIAM J Anal Math, 1999, 59: 1667--1685

[5] Farkas J Z. Stability conditions for a non-linear size-structured model. Nonlinear Anal RWA, 2005, 6: 962--969

[6] Farkas J Z, Hagen T. Stability and regularity results for a size-structured population model. J Math Anal Appl, 2007, 328: 119--136

[7] Gurtin M E, MacCamy R C. Nonlinear age-dependent population dynamics. Arch Rat Mech Anal, 1974, 54: 281--300

[8] Webb G F. Theory of Nonlinear Age Dependent Population Dynamics. New York: Marcel Dekker, 1985

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Stability of Equilibrium Solutions to Size-structured Population Models

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