On the dynamics of the q-Tsallis Gauss Iterated Map

We investigate the dynamical properties of a q-deformed generalization of the Gaussian iterated map, referred to as the q-Tsallis Gaussian Iterated Map, obtained by replacing the standard exponential with the Tsallis q-exponential function. Through bifurcation diagrams, Lyapunov exponent analysis, and isoperiodic diagrams, we characterize the transitions between periodic and chaotic regimes, as well as the emergence of multistability and bubbling phenomena, reveals that the introduction of the nonextensive parameter induces significant changes in the system’s dynamics.