Stochastic transition in synchronized spiking nanooscillators

Abstract

This work reports that synchronization of Mott material-based nanoscale coupled spiking oscillators can be drastically different from that in conventional harmonic oscillators. We investigated the synchronization of spiking nanooscillators mediated by thermal interactions due to the close physical proximity of the devices. Controlling the driving voltage enables in-phase 1:1 and 2:1 integer synchronization modes between neighboring oscillators. Transition between these two integer modes occurs through an unusual stochastic synchronization regime instead of the loss of spiking coherence. In the stochastic synchronization regime, random length spiking sequences belonging to the 1:1 and 2:1 integer modes are intermixed. The occurrence of this stochasticity is an important factor that must be taken into account in the design of large-scale spiking networks for hardware-level implementation of novel computational paradigms such as neuromorphic and stochastic computing.

Keywords: spiking oscillators; stochastic transition; synchronization evolution; thermal coupling; time domain phase coexistence.

Fig. 1.

Heat propagation between nanodevices. (A) SEM image with false color of four neighboring VO₂ devices. Each device is 500 × 500 nm². The devices are separated by a 500 nm gaps and are electrically isolated from each other. The first device (black) acts as a “heat generator”, while the other three (red, blue, and cyan) are “probes”. (B) Normalized resistance changes (ΔR/R₀) of the second, third, and fourth devices as a function of dissipated power in the first device. The measurements were performed at 327 K base temperature. The resistance decrease with increasing driving power indicates heat propagation from the first device that increases the temperature of the other devices.

Fig. 2.

Synchronization of spiking oscillators via thermal interaction. (A) Electrical circuit used to generate spiking oscillations in VO₂ nanodevices. The SEM image shows two neighboring VO₂ nanodevices. (B) Overlaid current traces showing incoherent spiking in two noninteracting VO₂ nanooscillators when they are biased with 8.4 V independently in two separate measurements. (C) Current traces showing coherent in-phase spiking in the same pair of nanooscillators as in B when they are biased with 8.4 V simultaneously.

Fig. 3.

Synchronized spiking pattern evolution. Current traces displaying spiking oscillations of two VO₂ nanodevices under different applied voltages. (A) 2:1 synchronization: two red spikes are locked to one black spike when 9.2 V is applied to the red oscillator and 7.8 V is applied to the black oscillator. (B) 1:1 synchronization: each red spike locks into each black spike when 9.2 V is applied to the red oscillator and 10 V to the black oscillator. (C) 1:2 synchronization: one red current spike locks into every second black spike when 3.2 V is applied to the red oscillator and 10 V is applied to the black oscillator. (D and E) Stochastic synchronization emerges at transitions between the modes at intermediate applied voltages. While spikes of the two oscillators overlap, random length spiking sequences corresponding to 2:1 and 1:1 modes (highlighted by green and blue backgrounds, respectively) emerge at random positions.

Fig. 4.

Stochastic synchronization regime. (A) Interspike interval (ISI) evolution of one oscillator at 3.7 V applied voltage when the neighboring oscillator is powered with 10 V at the same time. (B) 2:1 mode fraction as a function of applied voltage. The stochastic region appears between 3.3 V to 4.2 V. (C) Autocorrelation function (ACF) of two ISI sequences recorded at 3.7 V and 4.1 V. Before applying ACF, the ISI data were converted into binary sequences (see the description in the text).