The advanced Julia technique is designed to generate and explore inner wings within the wings generated through the classical Julia technique. These wings were further folded by applying the Julia technique in different coordinates to obtain a multifolded fractal structure. Therefore, in this paper a newly designed technique (advanced Julia) is used as a fractal technique following the route Formula: see text to find recurring trajectories inside spherical-shaped wings. For this, the Arneodo chaotic system is considered as an example, where both Julia-based techniques are applied to seek inner and outer multifolds. The results are further compared by plotting their corresponding bifurcation diagrams. It is observed that the usage of advanced Julia technique not only helps in generating inner wings but also has an impact on the overall dynamics. The analytical results are accompanied by simulations using MATLAB to visualize their phase portraits and time series.
Zulqarnain et al. (Fri,) studied this question.