Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network

Studying the firing dynamics and phase synchronization behavior of heterogeneous coupled networks helps us understand the mechanism of human brain activity. In this study, we propose a novel small heterogeneous coupled network in which the 2D Hopfield neural network (HNN) and the 2D Hindmarsh–Rose (HR) neuron are coupled through a locally active memristor. The simulation results show that the network exhibits complex dynamic behavior and is different from the usual phase synchronization. More specifically, the membrane potential of the 2D HR neuron exhibits five stable firing modes as the coupling parameter k1 changes. In addition, it is found that in the local region of k1, the number of spikes in bursting firing increases with the increase in k1. More interestingly, the network gradually changes from synchronous to asynchronous during the increase in the coupling parameter k1 but suddenly becomes synchronous around the coupling parameter k1 = 1.96. As far as we know, this abnormal synchronization behavior is different from the existing findings. This research is inspired by the fact that the episodic synchronous abnormal firing of excitatory neurons in the hippocampus of the brain can lead to diseases such as epilepsy. This helps us further understand the mechanism of brain activity and build bionic systems. Finally, we design the simulation circuit of the network and implement it on an STM32 microcontroller.