Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse

The memristor has drawn a significant interest in the fields of neuromorphic circuits because the nanoscale memristor is a strong candidate to become the critical element of novel ultra-high density low-power non-volatile memories. In the present paper, we focus on networks of FitzHugh-Nagumo neuron circuits employing memristor. First, we build the memristor-based circuit of FitzHugh-Nagumo model. The details of the chaotic phenomena of the memristor-based FitzHugh-Nagumo circuit under external stimuli have been found with use of computer simulations, i.e., we have numerically calculated waveform diagrams, phase portraits, Lyapunov exponents and bifurcation diagram. And we also confirm these results of theoretical analyses and numerical calculations by circuit simulation experiments of the actual analog circuit realization using Multisim modeling. Then the synchronization of coupled memristor-based chaotic neurons with memristor synapse is discussed, and synchronization mechanism is also found. Finally, we have also derived the sufficient conditions of chaotic synchronization in unidirectional coupled neuron circuits and bidirectional coupled neuron circuits respectively, which are that the parameter of memristor synapse must meet certain conditions. These results of theoretical analyses have been confirmed by numerical simulation.