Analysis of the dynamical behavior of discrete memristor-coupled scale-free neural networks

The synchronization of neural networks is crucial for neural information processing and represents a key feature of various functional brain diseases. Memristors are ideal electronic components for mimicking biological synapses, among which discrete memristors have the advantage of fast computing speed and are often used in memristor-based neural networks. For these reasons, this paper proposes a novel discrete memristor-coupled Scale-Free neural network (DMSNN). Phase diagrams and time series of membrane potential are employed to analyze the firing pattern coexistence of individual neurons in the network. Furthermore, Spatiotemporal patterns, heat maps of the Spearman correlation coefficient matrix and the values of neuron membrane potential at a particular time point are adopted to declare the spatio-temporal dynamics of the complex neural network, encompassing asynchronization, chimeric state, synchronization and synchronization transition. The study also identifies the phenomenon of topology-induced coexistence and elucidates the underlying reasons for the emergence of chimeric states in the DMSNN as the coupling strength increases. Finally, a hardware implementation platform is constructed using a highly integrated SSD202 processor to validate the accuracy of the DMSNN. The results are consistent with the numerical simulations.