An Emotional Model Constructed on a Chaotic Map Using 3D-Fractional Discrete-Time Analysis

By giving system dynamics more degrees of freedom, fractional discrete systems provide flexible modeling and control frameworks. The main dynamic characteristics of the 3D-fractional Layla and Majnun model (3D-LMM) are addressed in this study as we suggest and examine variations of the model. The presence of constant and asymptotically steady zero solutions is guaranteed by the necessary and sufficient conditions we define for the stability and asymptotic stability of the 3D-LMM. As a specific case, we analyze the system in terms of its equilibrium and fixed points, looking at the situation where Layla and Majnun have equal feelings. We demonstrate that, in the presence of marginal stability conditions, the system hovers on a precarious trajectory influenced by its fractional dynamics, neither convergent nor divergent, but on the edge between stability and instability.