Discrete Dynamical System

Discrete dynamical systems, which model systems evolving through discrete time steps, are a focus of current research aiming to improve their predictive power and understand their underlying structure. This involves developing and analyzing novel architectures like recurrent neural networks and spiking neural networks, often employing techniques such as gradient descent and spectral decomposition to optimize system behavior and achieve tasks like classification. Significant effort is dedicated to efficiently learning both the dynamics and topology of these systems from limited data, particularly in applications like contagion modeling and control problems. These advancements have implications for diverse fields, including artificial intelligence, network science, and robotics, by enabling more accurate and efficient modeling of complex systems.