Dynamical analysis of logistic map with feedback control, additive Allee effect, and harvesting with application in color image encryption
Mohammad Fahrurrozy, Agus Suryanto, İsnani Darti · Mathematics in Applied Sciences and Engineering · 2026
Chaotic property of dynamical systems is known to be exploited in image encryption scheme. In this paper, we study the chaotic property of a fractional order logistic map with feedback control, additive Allee effect, and harvesting. Dynamical analyses are discussed such as the existence and local stability of fixed points of the map. The study also establishes the existence of Neimark-Sacker and period-doubling bifurcation. With the intention to enhance the chaos complexity of the map, we modify the map by utilizing the cascade concept and modulo operation to become the fractional-order modified logistic map (FOMLM). Chaos complexity is analyzed with bifurcation diagram, chaos trajectories, and Lyapunov exponent. Subsequently, a FOMLM-based color image encryption scheme is proposed to establish the "permutation-diffusion" concept in the encryption scheme. Performance analysis of the scheme gives an indicator of robustness against cryptanalysis and is highly sensitive to the plain image and the secret key.