Synchronization generations and transitions in two map-based neurons coupled with locally active memristor

As a connecting synapse, memristor is considered as a feasible device for representing the magnetic induction between two coupled neurons to enable the information exchange. However, the effect of memristor as a coupling synapse between two map-based neurons on synchronous activity has not received sufficient attention. To this end, an extensible locally active memristor is proposed, and its various characteristics are demonstrated by several existing methods. Based on the proposed memristor and two map-based neurons, a memristor synapse-coupled neuron model is constructed to investigate the memristor-induced synchronous firing activities. Taking the coupling strength and memristor synapse initial state as controllable variables, several analysis methods, such as phase diagram, normalized mean synchronization error, similarity function, and phase difference, are used to clearly reveal various synchronization phenomena triggered by the introduced memristor, including complete synchronization, lag synchronization, and phase synchronization, as well as the accompanying spiking/bursting firing behaviors. In particular, the generation and transition of synchronization depend on the initial states of the memristor synapse-coupled neuron model, resulting in the coexistence of firing modes. The correctness of these synchronous firing activities is validated by digital hardware experiments. Numerical and hardware results show that the memristor, as a coupling synapse, provides a flexible and reliable control scheme for the synchronization between neurons.