Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics

TL;DR

This paper shows that large coupled bistable systems can detect very small heterogeneity with high sensitivity, where even a few non-identical elements can switch the entire system's state, useful for parallel search.

Contribution

The study reveals a sharp transition in collective response of coupled bistable elements, enabling ultra-sensitive detection of heterogeneity with scalable system size.

Findings

System response reflects presence of few non-identical elements

Critical fraction scales as 1/√N with system size

System achieves one-bit sensitivity to heterogeneity

Abstract

We demonstrate how the collective response of $N$ globally coupled bistable elements can strongly reflect the presence of very few non-identical elements in a large array of otherwise identical elements. Counter-intuitively, when there are a small number of elements with natural stable state different from the bulk of the elements, {\em all} the elements of the system evolve to the stable state of the minority due to strong coupling. The critical fraction of distinct elements needed to produce this swing shows a sharp transition with increasing $N$, scaling as $1/\sqrt{N}$. Furthermore, one can find a global bias that allows robust {\em one bit} sensitivity to heterogeneity. Importantly, the time needed to reach the attracting state does not increase with the system size. We indicate the relevance of this ultra-sensitive generic phenomenon for massively parallelized search applications.