Dynamics, circuit design, feedback control of a new hyperchaotic system and its application in audio encryption

In this study, a 4D hyperchaotic system is constructed based on the foundation of a 3D Lü chaotic system. The newly devised hyperchaotic system possesses a sole equilibrium point, showcasing a simplified system structure that reduces complexity. This simplification offers a clearer opportunity for in-depth analysis of dynamic behaviors in the realm of scientific research. The proposed hyperchaotic system undergoes an in-depth examination of its dynamical characteristics, including chaotic attractors, equilibrium point stability, Lyapunov exponents' spectrum, and bifurcation diagram. Numerical analysis results reveal that the attractor of this hyperchaotic system exhibits highly complex, non-periodic, and fractal structural dynamics. Its motion demonstrates extreme sensitivity and randomness, even within a wide range of variations in parameter d, affirming its hyperchaotic properties with two positive Lyapunov exponents. Hyperchaotic bifurcation diagrams typically exhibit highly intricate structures, such as fractals, branches, and period doubling characteristics, signifying that even minor parameter adjustments can lead to significant changes in system behavior, presenting diversity and unpredictability. Subsequently, to further investigate the practical utility of this hyperchaotic system, a linear feedback control strategy is implemented. Through linear feedback control, the hyperchaotic system is stabilized at its unique equilibrium point. Experimental validation is conducted using both computer software simulation Matlab, electronic circuit simulation Multisim, and embedded hardware STM32. The results of these experiments consistently align, providing theoretical support for the application of this hyperchaotic system in practical domains. Finally, leveraging the hyperchaotic keys generated by this hyperchaotic system, audio encryption is achieved using a cross-XOR algorithm, which is then realized on the embedded hardware platform STM32. The results show that the audio encryption scheme based on the hyperchaotic system is feasible, and the method is simple to implement, has nonlinear characteristics and certain algorithm complexity, which can be applied to audio encryption, image encryption, video encryption, and more.