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

TL;DR

This paper analyzes the synchronization behavior of two identical MIT-based relaxation oscillators with charge-based coupling, revealing phase-locking phenomena, bistability, and complex dynamics relevant for low-power computing applications.

Contribution

It provides a detailed theoretical and experimental study of synchronization in MIT device oscillators, introducing new insights into phase relationships and bistability in coupled systems.

Findings

In D-D configuration, oscillators synchronize in anti-phase with capacitive coupling.

Resistive coupling leads to in-phase synchronization.

Bistability occurs for certain coupling parameters, enabling potential associative computing applications.

Abstract

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.