# Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations

arXiv: https://arxiv.org/abs/2004.04769 · HTML: https://mlsanity.com/paper/2004.04769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)

## Abstract (arXiv)

Chimera states arising in the classic Kuramoto system of two-dimensional phase coupled oscillators are transient but they are "long" transients in the sense that the average transient lifetime grows exponentially with the system size. For reasonably large systems, e.g., those consisting of a few hundreds oscillators, it is infeasible to numerically calculate or experimentally measure the average lifetime, so the chimera states are practically permanent. We find that small perturbations in the third dimension, which make system "slightly" three-dimensional, will reduce dramatically the transient lifetime. In particular, under such a perturbation, the practically infinite average transient lifetime will become extremely short, because it scales with the magnitude of the perturbation only logarithmically. Physically, this means that a reduction in the perturbation strength over many orders of magnitude, insofar as it is not zero, would result in only an incremental increase in the lifetime. The uncovered type of fragility of chimera states raises concerns about their observability in physical systems.