Synchronization transitions in a discrete memristor-coupled bi-neuron model

When synaptic connection is created to couple two neurons, the electromagnetic induction current is unavoidably induced, which can be imitated by a flux-controlled memristor. To construct a discrete model of coupled neurons, a discrete memristor is used to couple two Rulkov maps bidirectionally and a discrete synapse is obtained. This discrete bi-neuron model composed of two map neurons has infinitely many fixed points. The synchronization behaviors are detected by calculating normalized synchronization error, and the memristive effects and dynamical behaviors are investigated by using bifurcation diagrams and phase trajectories. The results show that the discrete bi-neuron model can generate complete and lag synchronization behaviors, and the transitions of spiking-bursting firings and synchronizations are strongly affected by the coupling strength and initial state of the coupled channel embedded with memristor. In particular, the synchronization transitions via memristor coupling demonstrate the coexistence of multiple firing patterns of the discrete bi-neuron model and manifest the realization of synchronous control of coupled neurons. All these meaningful phenomena are verified by digital hardware experiments.