A new fractional-order chaos system of Hopfield neural network and its application in image encryption

• A new model of fractional-order HNN system is proposed. • The chaos performance of the proposed system is analyzed. • The new encryption algorithm is designed based on the proposed fractional-order HNN system, and the NIST test is tested. • The security of the algorithm such as NPCR, UACI are compared and analyzed. In this work, we propose a new fractional-order chaotic system based on the model of 4-neurons-based Hopfield Neural Network (HNN). By using Adomain decomposition method, the proposed fractional-order chaotic system is solved. With the orders changing, the proposed fractional-order system shows rich dynamical characteristics. Then, based on the pseudo-random numbers (PRNs) generated by the proposed system, a new construction method of multiple hash index chain is designed. And a new image encryption algorithm is designed according to the multiple hash index chain. The safety test results show that the design encryption algorithm has higher security performance. Finally, the 4-neurons-based HNN fractional-order system is implemented by Multisim circuit simulation. The experimental results show the feasibility of the theoretical analysis.