  Computing with networks of synchronous oscillators has attracted wide-spread
attention as novel materials and device topologies have enabled realization of
compact, scalable and low-power coupled oscillatory systems. Of particular
interest are compact and low-power relaxation oscillators that have been
recently demonstrated using MIT (metal- insulator-transition) devices using
properties of correlated oxides. This paper presents an analysis of the
dynamics and synchronization of a system of two such identical coupled
relaxation oscillators implemented with MIT devices. We focus on two
implementations of the oscillator: (a) a D-D configuration where complementary
MIT devices (D) are connected in series to provide oscillations and (b) a D-R
configuration where it is composed of a resistor (R) in series with a
voltage-triggered state changing MIT device (D). The MIT device acts like a
hysteresis resistor with different resistances in the two different states. The
synchronization dynamics of such a system has been analyzed with purely charge
based coupling using a resistive (Rc) and a capacitive (Cc) element in
parallel. It is shown that in a D-D configuration symmetric, identical and
capacitively coupled relaxation oscillator system synchronizes to an anti-phase
locking state, whereas when coupled resistively the system locks in phase.
Further, we demonstrate that for certain range of values of Rc and Cc, a
bistable system is possible which can have potential applications in
associative computing. In D-R configuration, we demonstrate the existence of
rich dynamics including non-monotonic flows and complex phase relationship
governed by the ratios of the coupling impedance. Finally, the developed
theoretical formulations have been shown to explain experimentally measured
waveforms of such pairwise coupled relaxation oscillators.
