Complex synchronization in memristor-coupled Chialvo Neurons

The study of neurons and their interaction mechanisms plays a critical role in advancing our understanding of brain functionality and neural network dynamics. Recent studies demonstrated that memristor-based neural networks can effectively simulate biological neural behaviors and exhibit rich dynamical properties. In this paper, we propose a tanh-type memristor-coupled Chialvo neuron model and investigate its dynamic behaviors and synchronization patterns under varying parameter conditions. We demonstrate that fine-tuning the external excitation current can effectively regulate the synchronization state between neurons, highlighting the potential of memristors in controlling neural network synchronization. Using the Hilbert transform, we construct analytic signals to extract the instantaneous phase spectra of the membrane potentials of two coupled neurons. The phase difference is calculated by subtracting the instantaneous phases, and a synchronization coefficient is introduced to quantify the degree of synchronization. Finally, the validity of our findings is confirmed through experimental implementation on a CH32 microcontroller.