Almost Periodic Dynamic of a Discrete Wazewska-Lasota Model

Yoshihiro Hamaya


The purpose of this article is to investigate the existence of an almost periodic solution of a discrete Wazewska-Lasota model involving a linear harvesting term\[x(n+1)-x(n)= -\alpha(n)x(n+1) +\sum_{i=1}^{l}\beta_{i}(n)e^{-\gamma_{i}(n)x(n-\tau_{i}(n))}-H(n)x(n-\sigma(n)),\] by using the contraction mapping principle, and we also show that the solution of above equation converge exponentially to an almost periodic solution by constructing a luxury Liapunov functional.


Almost periodic solutions; Wazewska-Lasota model; Exponential dichotomy; Liapunov functional

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J.O. Alzabut, Y. Bolat and T. Abdeljawad, Almost periodic dynamic of a discrete Nicholson's blowflies model involving a linear harvesting term,

Advances in Difference Equations, to appear.

L. Berezansky, E. Braverman and L. Idels, Nicholson's blowflies differential equations revisited: Main results and open problems,

Appl. Math. Modelling 34 (2010), 1405-1417.

C. Corduneanu, Almost periodic discrete processes, Libertas Mathematica 2 (1982), 159-169.

C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, 2009.

S. Elaydi, An Introduction to Difference Equations, 3rd edition, Springer, 2005.

Y. Hamaya, Global attractivity in Wazewska-Lasota difference model, Differential Equations and Dynamical Systems 5 (2) (1997), 187-195.

T. Itokazu and Y. Hamaya, Almost periodic solutions of prey-predator discrete models with delay, Advances in Differene Equations, (2009), Article ID 976865.

G. Karakostas, Ch.G. Philos and Y.G. Sficas, The dynamics of some discrete population models, Nonlinear Anal. TMA 17 (1991), 1069-1084.

S. Murakami and Y. Hamaya, Global attractivity in an integrodifferential equation with diffusion, Differential Equations and Dynamical Systems 3 (1) (1995), 35-42.

M. Wazewska-Czyzewska and A. Lasota, Mathematical problems of the dynamies of the red blood cells system, Ann. Polish Math. Soc. Ser. III. Appl. Math. 6 (1976), 23-40.

T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Applied Mathematical Sciences 14, Springer-Verlag, 1975.

C. Zhang, Almost Periodic Type Functions and Ergodicity, Science Press/Kluwer Academic Publishers, 2003.



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