Dynamics and chaos control of <i>q</i> -deformed Gaussian map via superior approach

This study introduces a deformation framework applied to the classical Gaussian map, yielding a q-deformed Gaussian map with enhanced dynamical properties. The analysis focuses on the nonlinear characteristics, bifurcation patterns, and topological entropy of the deformed system. Through analytical methods and visual tools like Lyapunov exponents and bifurcation diagrams, the q-deformed map demonstrates an expanded stability compared to its classical counterpart. Furthermore, to control chaotic dynamics in both classical and deformed Gaussian maps, a two-step feedback control mechanism is implemented. This approach stabilizes unstable periodic orbits and suppresses chaos effectively, as validated through numerical simulations.