Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristor

The number of attractors in a memristor-based multiscroll Hopfield Neural Network (HNN) is typically coupled with the number of polynomials, which leads to a coupling between the computational complexity and resource utilization in circuit implementation. To decouple this relationship, we propose a non-polynomial memristor that satisfies the Lipschitz condition. Regardless of whether it is used to simulate synaptic behavior, simulate the impact of electromagnetic radiation, or a combination of both scenarios, it can conveniently control the generation of single-direction or multiple-direction multiscroll attractors without adding or reducing any terms. By constructing Lyapunov functions, the sufficient condition for these multiscroll memristor HNNs to be bounded is obtained. After improving the feasibility of linear matrix inequalities, a strongly adaptive observer is proposed. After uniting an adaptive sliding mode control method, we propose a new adaptive synchronization scheme to simulate neural network synchronization. Finally, the digital circuit implementation and functional verification of these memristor-based multiscroll HNNs are completed using a field-programmable gate array (FPGA). Based on this, an image encryption circuit is designed so that the FPGA can directly encrypt images and transmit them to the IO device.