The Julia technique facilitates the transformation of a chaotic system of ordinary differential equations (ODEs) into its corresponding normal (prototype) form. These prototype forms help in generating additional wings and extending the complexity of the dynamics. In this paper, the Julia technique is applied to a chaotic system to visualize these additional wings. Subsequently, based on ring topology, the considered system is converted into networks using coupling terms. For this purpose, we consider a conservative chaotic system, to which the Julia transformation technique is applied in order to obtain its prototype form. The original chaotic system and its prototype are each converted into networks consisting of 𝜂-oscillators. Furthermore, the dynamics of four systems-namely, the original system, the prototype system, and their corresponding networks-are explored using bifurcation diagrams, Lyapunov exponents, and basins of attraction.
Wang et al. (Tue,) studied this question.