Memristor-induced hyperchaos, multiscroll and extreme multistability in fractional-order HNN: Image encryption and...

Fractional-order differentiation (FOD) can record information from the past, present, and future. Compared with integer-order systems, FOD systems have higher complexity and more accurate ability to describe the real world. In this paper, two types of fractional-order memristors are proposed and one type is proved to have extreme multistability, local activity, and non-volatility. By using memristors to simulate the autapse of a neuron and to describe the phenomenon of electromagnetic induction caused by electromagnetic radiation, we establish a new 5D FOD memristive HNN (FOMHNN). Through dynamic simulation, rich dynamic behaviors are found, such as hyperchaos, multiscroll, extreme multistability, and "overclocking" behavior caused by order reduction. To the best of our knowledge, this is the first time that such rich dynamic behaviors are found in FOMHNN simultaneously. Based on this FOMHNN, a very efficient and secure image encryption scheme is designed. Security analysis shows that the encrypted Lena image has extremely low adjacent pixel correlation and high randomness, with information entropy of 7.9995. Despite discarding diffusion and scrambling, it has excellent plaintext sensitivity, with NCPR = 99.6095% and UACI = 33.4671%. Finally, this paper implements the proposed FOMHNN and image encryption on field programmable gate array (FPGA). To our knowledge, the related work of fully hardware implementation of fractional-order neural networks and image encryption schemes based on this is rare.