Dual Memristor-Coupled Hopfield Neural Network With Any Multi-Scroll Amplitude Control and Its Application for Medical Image Classification

Sen Zhang, Dazhe He, Yongxin Li, Daorong Lu, Chunbiao Li

Abstract: In practical applications, effectively regulating the amplitude of chaotic signals and maintaining the chaotic nature of the system are extremely critical to ensure system stability and prevent failures. However, traditional amplitude control methods usually change the bifurcation threshold or attractor geometry, impairing the integrity of chaos and increasing the risk of system instability, thus struggling to achieve effective control over complex chaotic signals. Given the rapid advancement in brain-inspired intelligence technology, it has become imperative to investigate new control techniques based on memristors to overcome the limitations of conventional approaches. To address these challenges, in this paper, a novel dual memristor-coupled Hopfield Neural Network (DMCHNN) is established, where one memristor represents external electromagnetic radiation and the other mimics synaptic connections. Two independent amplitude controllers are devised for signal rescaling, being capable of adjusting signal amplitudes in various modes, such as single-scroll, double-scroll, multi-double-scroll and coexisting homogeneous multi-scroll attractors induced by initial offset boosting. Simulations indicate that the parameter operating range of the amplitude controllers can reach up to ${10}^{5}$ or beyond. Furthermore, the performance of the amplitude controllers is additionally verified through the implementation based on the CH32 microcontroller. Rescaled chaotic signals are evaluated to determine their robust effectiveness in the deployment of pseudo-random number generators (PRNG). Eventually, the multi-scroll chaotic data with different amplitudes generated from DMCHNN is fed into the optimization algorithms for neural network optimization, which is utilized for medical image classification. Note to Practitioners—This work is motivated by utilizing the unique advantages of memristors to achieve amplitude control of complex chaotic signals in neural networks and enhance their modulation range to meet the requirements of practical engineering applications. Nevertheless, the majority of the existing control approaches are aimed at the amplitude control of single- and double-scroll within a limited range, and have less engagement in the amplitude control of relatively complex multi-scroll and coexisting multi-scroll chaotic signals. To overcome this challenge, this paper concurrently employs the synaptic plasticity and electromagnetic radiation effects of the memristors to construct a novel dual memristor-coupled Hopfield neural network (DMCHNN). The DMCHNN can not only achieve the modulation of single- and double-scroll chaotic signals via memristors, but also regulate the amplitudes of multi-scroll as well as the initial offset enhancement-induced homogeneous multi-scroll attractors. More significantly, these amplitude controllers have parameter control ranges of ${10}^{5}$ or larger, that is, realizing ultra-large-scale amplitude control of diverse chaotic signals. This presents a new control technique for the regulation of chaotic signals. Finally, the multi-scroll chaotic data with different amplitudes generated by DMCHNN is combined with the neural network optimization algorithm, which is successfully used for medical image classification and demonstrates outstanding performance, providing novel ideas and solutions for the field of image processing.