Computational Analysis of a Nonautonomous Incommensurate Fractional-Order Swing System: Chaos, Control, and Image Cryptography

Abstract

In this paper, the dynamic behavior of an incommensurate fractional-order single-machine infinite-bus (IFOSMIB) power system is investigated through numerical simulations. Different dynamical phenomena are observed in the IFOSMIB system, including periodic oscillations, period-doubling bifurcations, and chaotic attractors. Furthermore, the complexity of the system dynamics is quantified using the complexity measure C₀. In addition, the positivity of the largest Lyapunov exponent (LLE) and the results of the 0–1 test for chaos, a robust indicator for distinguishing regular dynamics from chaotic dynamics, confirm the existence of chaos in the system. Moreover, an effective control scheme is proposed to suppress the chaotic oscillations of the IFOSMIB power system, and its effectiveness is verified through numerical simulations. Furthermore, the proposed fractional-order chaotic system is investigated for information security applications. Its complex and highly sensitive dynamics are exploited in the development of a chaos-based encryption scheme, in which the generated chaotic sequences are employed for secure data encryption. The obtained results demonstrate the potential of the proposed system for cryptographic and secure communication applications.