A novel fractional-order 3-D chaotic system and its application to secure communication based on chaos synchronization

Abstract In this study, we introduce a new fractional-order chaotic system (FO-CS) that comprises six terms, setting it apart from classical chaotic models such as the Lorenz, Chen, and Lü systems. The proposed system, while having a different number of terms compared to the Lorenz and Chen systems, generates attractors that closely resemble those found in these conventional systems. The algebraic structure of the system is relatively simple, consisting of four linear terms and two quadratic terms. We conduct a comprehensive theoretical analysis and dynamic simulations of the system from both fractional and integer-order perspectives, exploring numerous dynamical characteristics, including Lyapunov exponent spectra, fractal dimensions, Poincaré maps, and bifurcation phenomena. Furthermore, we derive the Hamiltonian energy function for the proposed system through the application of Helmholtz’s theorem. To delve into synchronization within the system, we carry out numerical simulations alongside an active control method. The effective implementation of synchronization through this control strategy deepens our understanding of system dynamics and highlights its potential applications, particularly in secure communication. One significant application is the use of synchronization techniques for the secure transmission of real audio signals, showcasing the relevance of synchronization technique in enhancing communication security.