On the Weighted Piecewise Pseudo Almost Automorphic Solutions Mackey-Glass Model With Mixed Delays and Harvesting Term

Abstract

In the present work, we employ the new concept of weighted piecewise pseudo almost automorphic functions and study the impulsive Mackey-Glass model with mixed delays and nonlinear harvesting term. First, we give essential lemmas and some composition theorems related to the considered space. Second, by a suitable fixed-point theorem and the properties of the weighted piece-wise pseudo almost automorphic space, the existence and uniqueness of the weighted piecewise pseudo almost automorphic solutions are established. Furthermore, by Gronwall inequality and impulsive differential inequalities, we obtained the exponential, asymptotic stability of the weighted piecewise pseudo almost automorphic solutions. Finally, four examples and their numerical simulations are given to illustrate that the obtained results are feasible and effective.