The Caputo-like discrete fractional video motion system with artificial neural networks: Chaos, stabilization and synchronization

This paper investigates the chaotic dynamics of a three-dimensional video motion system modeled using artificial neural networks within the framework of Caputo-like discrete fractional calculus. Both commensurate and incommensurate fractional orders are considered. Particular attention is given to the dynamical properties of the system, which are characterized through the coexistence of multiple attractors, bifurcation structures, and the evaluation of Lyapunov exponents. The stability of the proposed model is examined at a fixed point under both types of fractional orders, employing numerical computations and simulations to validate the analysis. The main contribution of this work is the introduction of a Caputo-like discrete fractional artificial neural network model for video motion dynamics, which incorporates memory effects and leads to richer nonlinear behavior than classical integer-order models.