Solution to a high-performance incommensurate exponential oscillator system and its FPGA implementation for video encryption

This paper proposes a novel incommensurate exponential oscillator (IEO) system, which significantly enhances system performance through the incorporation of exponential nonlinear terms. Analytical solutions are derived using the Adomian decomposition method (ADM), and rigorous proofs of the existence and uniqueness of the system’s solutions are provided thereafter. Furthermore, the paper demonstrates the coexistence of multiple attractor types within the system while quantifying the impact of ADM expansion terms on computational accuracy. Subsequently, a rigorous comparison of the Lyapunov exponents of this system with those of analogous systems demonstrates the performance advantages of the proposed IEO system. In addition, this paper introduces a hardware-friendly discrete ADM (HD-ADM) for the first time, contrasting its performance with prevailing solution approaches. Finally, its application in video encryption based on FPGAs is demonstrated, highlighting the proposed HD-ADM’s broad application prospects.