Variance-based control of regime shifts: bistability and oscillations

TL;DR

This paper explores how variance-based control can manage regime shifts, bistability, and oscillations in systems, focusing on the effects of observation time-scale, feedback sensitivity, and noise on control effectiveness.

Contribution

It extends early warning signal methods by using variance to control long-term dynamics in bistable and oscillatory systems, analyzing key influencing factors.

Findings

Variance control influences long-term system behavior

Observation time-scale affects control success

Noise intensity impacts control efficiency

Abstract

A variety of real world and experimental systems can display a drastic regime shift, as the evolution in one its paramaters crosses a threshold value. Assimilation of such a transition with a bifurcation has allowed to identify so called "early warning signals", at the level of the time series generated by the system underscope. The literature in early warning detection methods is currently expanding and their potential for practical applicability is being discussed in different contexts. In this work, we elaborate on the use of the variance of a system variable, which constitutes the simplest early warning indicator, to gain control on the long-term dynamics of the system, while extending an exploitation phase. In particular, we address the cases of the cusp and Hopf normal forms, as prototypical examples of bistability and oscillations. Our results provide insights on the interplay between the time-scale for the system observation, the degree of sensitivity of the control feedback and the intensity of the random perturbations, in shaping the long-term control efficiency.