Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: Analysis, amplitude controls, random number generator, and image encryption application

Abstract

Abstract Robust chaotic systems offer unpredictability, complex dynamics, noise-like properties, efficient bifurcation behavior, and the ability to model real-world phenomena, making them valuable in diverse scientific and engineering applications. This paper details on the dynamical appraisal, amplitude controls, microcontroller execution, Random number generator (RNG) of an autonomous three-dimensional (3D) oscillator with two and four wings attractors (ATDOTFWA), and its image encryption application. Thanks to the Routh-Hurwitz criteria, five steady states found in the ATDOTFWA are classified as stable or unstable, depending on its two control parameters. During the numerical simulations employing the Runge-Kutta scheme, the ATDOTFWA exhibit a wide range of dynamic behaviors, including no oscillations, Hopf bifurcation, limit cycle, five distinct presentations of two wings chaotic structures, monostable and bistable two wings chaotic structures, bistable and monostable regular oscillations, chaotic bursting characteristics, coexistence of period-2-oscillations and four wings chaotic structure, and four wings chaotic attractor which were validated experimentally by the microcontroller implementation. The total and partial controls of the amplitude are achieved in the ATDOTFWA. A RNG is designed based on the ATDOTFWA, and the generated random numbers are successfully tested using the ENT and NIST 800-22 statistical test suites, demonstrating the reliability of the ATDOTFWA-based RNG. This reliability is further confirmed through the application of the ATDOTFWA-based RNG in an efficient and secure image encryption process, where the generated random numbers are used as the encryption key. The effectiveness of the image encryption process is validated through comprehensive cryptanalysis, with an encryption time of 0.1923 s for a 512×512 image, an average normalized pixel change rate (NPCR) of 99.6126%, an average unified average changing intensity (UACI) of 33.4578%, and an average information entropy of 7.9994.