Dynamics of $q$-Deformed Logistic Map via Superior Approach - Renu,; Ashish,; Chugh, Renu (Journal of Applied Nonlinear Dynamics, 2026)
Inspired by various studies on $q$-deformations in physical systems and their wider applications in different fields, we study the $q$-deformed logistic map via a superior fixed-point feedback approach. Different dynamical characteristics such as fixed-points, time-series evolution, period-doubling bifurcation, and Lyapunov exponent of the system are analyzed using a superior approach. The results are carried out analytically as well as experimentally. Under the proposed approach, due to the presence of an additional control parameter $α$, the system exhibits superior dynamical characteristics such as better stability range, suitable lower maximum Lyapunov exponent value, and an improved sensitivity as compared to the traditional approach.