Analysis of Controllability and Stability in Nonlinear Discrete Dynamical Systems Through Functional Analytic Methods

Abstract

Infinite-dimensional systems are often employed to model various phenomena, including propagation and transport processes, as well as population dynamics such as reproduction, development, and extinction. In economic systems, delays are inherent due to the time lapse between decisions and their impacts. Similarly, in communication networks, data transmission involves a non-zero time interval between initiation and delivery. Sometimes, these delays arise from simplifications in the model. These systems are characterized by their energetics, which can be described using difference equations that incorporate historical data of the system. Numerous numerical methods exist to represent such systems.