Design, analysis, and application of a fractional-order multi-scroll chaotic system

Abstract The development of complex topological structures and enhanced pseudo-randomness in multi-scroll chaotic systems is critical for advancing chaos-based technologies and applications. In this study, a novel fractional-order multi-scroll chaotic system is proposed. By incorporating a fractional-order differential operator into the classical integer-order Chua system and constructing continuous nonlinear functions, the number and distribution of saddle-focus equilibria are systematically controlled, facilitating the generation of both unidirectional and grid-type multi-scroll attractors. The system is solved using Adomian Decomposition Method (ADM), and its dynamics are investigated through phase portraits, Lyapunov exponent spectra, bifurcation diagrams, and Poincaré sections. The numerical simulations reveal a rich array of dynamical behaviors and high complexity. Hardware-based experimental validation using a digital signal processor (DSP) further substantiates the physical realizability of the proposed model. Moreover, a novel fractional-order ordinary differential neural network (FODNN) is developed to learn the system’s dynamics, achieving accurate long-term predictions of chaotic trajectories with an error feedback strategy. The strong agreement among theoretical analysis, numerical simulation, and experimental validation confirms both the efficacy of the design methodology and its potential applications in secure communication and chaotic signal prediction.