Fractional order 1D memristive time-delay chaotic system with application to image encryption and FPGA implementation

The memristive chaotic systems have attracted much attention and have been thoroughly discussed. The analysis shows that the fractional-order system is closer to the real system, and the time-delay chaotic systems are of an infinite-dimension with high randomness and unpredictability. Here we consider these three concepts (time delay, fractional order and memristive) to propose a 1D time delay fractional order memristive chaotic system. The analysis of the system is investigated by theoretical analyses and numerical simulations using the Kumar algorithm based on the Caputo definition for fractional order. The results indicate that the system parameter can significantly affect the dynamic behavior, which can be indicated by bifurcation diagrams, Lyapunov exponent diagrams, and phase portraits. A numerical method is adapted here to simulate the system, enabling short-memory implementation using a field-programmable gate array (FPGA). The experimental results were in good agreement with the numerical simulation results. Furthermore, an image encryption scheme based on multi-level diffusion and multi-round diffusion–confusion was developed, which involves diffusion and confusion operations. Security analysis shows the effectiveness of the proposed algorithm in terms of high security and excellent encryption performance.