Stability and approximation of almost automorphic solutions on time scales for the stochastic Nicholson's blowflies model

Abstract

The stability and approximation of solutions of Nicholson’s blowflies model for the stochastic case on time scales is discussed. Using various tools of analysis, sufficient conditions for the existence of a square mean almost automorphic solution are derived. The randomness and time scales make the model a hybrid model, which is more realistic and useful. The analysis works for both discrete and continuous cases, as well as for several other cases such as quantum and Cantor sets. We establish appropriate conditions and results to explore the Ulam–Hyers–Rassias stability. Furthermore, the model with piecewise constant argument is analyzed. Then the approximate solution and a nicer bound of this model using the discretization method is established. We conclude with an example to demonstrate our analytical results.