Existence and stability of a mathematical model solution of classical brain metabolite variations in the circadian rhythm

This research aims to study an important model in view of its applications to brain metabolite variations in the circadian rhythm. We will discuss the solution existence and stability of the general form of this model and give its solution by using numerical and analytical methods. The numerical method is the proposed numerical method (El- Sayed method), and two analytical methods, the Adomian decomposition method (ADM) and the Picard method (PM). The uniqueness of the solution will be proved, the convergence of the series solution will be discussed, and an error analysis will be given. The numerical solution of the brain model (BM) in four different cases will be discussed.