Collective dynamics and memory-induced long-range order in spiking oscillator arrays*

Recent work has experimentally demonstrated a new class of spiking oscillators known as "thermal neuristors," [1] which operate through thermal interactions between adjacent vanadium dioxide resistive memories. Using numerical simulations, we demonstrate that an array of these thermal neuristors exhibits a wide range of collective behaviors. By adjusting the memory strength and external inputs, we observe a variety of phases, including strong correlations, scale-free clusters, disordered states, as well as bifurcations and chimera states. Our analysis reveals that memory plays a crucial role in shaping these collective dynamics, and we provide an analytical understanding that, despite local interactions, an adequate amount of memory results in long-range order across the array. Our findings pave the way for future experiments aimed at observing these intriguing states.