Discrete neuron models and memristive neural network mapping: A comprehensive review

In recent years, discrete neuron and discrete neural network models have played an important role in the development of neural dynamics. This paper reviews the theoretical advantages of well-known discrete neuron models, some existing discretized continuous neuron models, and discrete neural networks in simulating complex neural dynamics. It places particular emphasis on the importance of memristors in the composition of neural networks, especially their unique memory and nonlinear characteristics. The integration of memristors into discrete neural networks, including Hopfield networks and their fractional-order variants, cellular neural networks and discrete neuron models has enabled the study and construction of various neural models with memory. These models exhibit complex dynamic behaviors, including superchaotic attractors, hidden attractors, multistability, and synchronization transitions. Furthermore, the present paper undertakes an analysis of more complex dynamical properties, including synchronization, speckle patterns, and chimera states in discrete coupled neural networks. This research provides new theoretical foundations and potential applications in the fields of brain-inspired computing, artificial intelligence, image encryption, and biological modeling.