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Computing with networks of synchronous oscillators has attracted wide-spreadattention as novel materials and device topologies have enabled realization ofcompact, scalable and low-power coupled oscillatory systems. Of particularinterest are compact and low-power relaxation oscillators that have beenrecently demonstrated using MIT (metal- insulator-transition) devices usingproperties of correlated oxides. This paper presents an analysis of thedynamics and synchronization of a system of two such identical coupledrelaxation oscillators implemented with MIT devices. We focus on twoimplementations of the oscillator: (a) a D-D configuration where complementaryMIT devices (D) are connected in series to provide oscillations and (b) a D-Rconfiguration where it is composed of a resistor (R) in series with avoltage-triggered state changing MIT device (D). The MIT device acts like ahysteresis resistor with different resistances in the two different states. Thesynchronization dynamics of such a system has been analyzed with purely chargebased coupling using a resistive (Rc) and a capacitive (Cc) element inparallel. It is shown that in a D-D configuration symmetric, identical andcapacitively coupled relaxation oscillator system synchronizes to an anti-phaselocking state, whereas when coupled resistively the system locks in phase.Further, we demonstrate that for certain range of values of Rc and Cc, abistable system is possible which can have potential applications inassociative computing. In D-R configuration, we demonstrate the existence ofrich dynamics including non-monotonic flows and complex phase relationshipgoverned by the ratios of the coupling impedance. Finally, the developedtheoretical formulations have been shown to explain experimentally measuredwaveforms of such pairwise coupled relaxation oscillators.

Synchronization of pairwise-coupled, identical, relaxation oscillators based on metal-insulator phase transition devices: A Model Study