Design and OGY Stabilization of a 3-D Continuous-Time Chaotic System for 16-bit Audio Encryption

OpenAlex · English

The exploration of continuous-time chaotic systems remains a critical frontier in nonlinear dynamics, offering profound implications for secure communications, cryptography, and complex system control. This research presents a comprehensive investigation into a newly proposed three-dimensional (3D) continuous-time chaotic system characterized by unique hyperbolic tangent and absolute value nonlinearities. The mathematical architecture is analyzed to ascertain fundamental dynamical properties, including dissipativity, phase space topology, equilibrium structure, Lyapunov exponent spectrum, and bifurcation behaviors. The analysis reveals two non-trivial saddle-foci satisfying the necessary Shilnikov-type condition and a self-excited, effectively monostable chaotic attractor. To demonstrate controllability, the Ott-Grebogi-Yorke (OGY) method is implemented through a fully numerical, map-level linearization suited to the non-smooth flow; the chaotic trajectory is stabilized onto a target Unstable Periodic Orbit (UPO) with a remarkably low control effort of 8.7952 units. Furthermore, the chaotic dynamics are leveraged to develop a secure digital audio encryption algorithm built on a plaintext-dependent permutation–diffusion architecture. Security analyses across speech, music, and environmental datasets reveal near-zero correlation, a Shannon entropy of 13.14 in the 16-bit space, NPCR and UACI satisfying the appropriate statistical criteria, demonstrated resistance to known-/chosen-plaintext attacks, and a key space of $2^{186}$ . The framework is further shown to extend to 8-bit image encryption.