Synchronization phenomena of two nonlinear oscillator systems when coupled through a memristor are analyzed exhaustively. Due to the presence of the memristor the coupling is nonlinear and very similar to a synaptic coupler. Study of such systems are now a days extremely important due to the recent thrust on neuromorphic computing which tries to replicate the principles of operation of human brain, where a series of such systems either coupled in series or in parallel are used. Here we have considered Lorenz and Hindmarsh-Rose systems in particular. They are analyzed by numerical simulations. They are also analyzed experimentally through electronic circuits. For the experimental part, the memristor is replaced with the equivalent op-amp combination. The most striking phenomenon observed is that the synchronization shows an intermittent character with respect to parameter variations due to the existence of complex basin structure with more than one attractor. Another new aspect of this type of synchronization is its sensitive dependence on initial conditions which is due to the existence of complex basin structure with more than one attractor. As such a totally new type of synchronization is observed and explored.