Emergence of synchronization in bio-inspired memristor-coupled oscillatory cells

The nanoscale memristor is a serious candidate to become the core element of novel ultra-high density low-power non-volatile memories and innovative pattern recognition systems based upon oscillatory associative and dynamic memories. Furthermore, this peculiar device also has the potential to capture the behavior of a biological synapse more efficiently and accurately than any conventional electronic emulator since it exhibits the unique capability of performing computation and storing data at the same physical location and at same time. In addition, it has a flux-controlled conductance which is analogous to the ionic flow-controlled synaptic weight. This chapter gives some insight into the mechanisms underlying the emergence of synchronization between two oscillatory cells coupled through an ideal memristor. The investigations show that in some cases the nonlinear dynamics of the memristor play a key role in the development of synchronous oscillations in the two oscillators. This work sheds light on some aspects of the nonlinear behavior of the still largely unexplored memristor, which is doomed to make an impact in integrated circuit design in the years to come.