Almost Periodic Dynamic of a Discrete Wazewska-Lasota Model - Hamaya, Yoshihiro (Communications in Mathematics and Applications, 2014)
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.
Keywords: Almost periodic solutions; Wazewska-Lasota model; Exponential dichotomy; Liapunov functional