Data-Driven Model Identification Near a Supercritical Hopf Bifurcation Using Phase-Based Approaches

TL;DR

This paper introduces a data-driven method for identifying models of systems near a supercritical Hopf bifurcation using phase-based techniques, enabling efficient parameter inference and control design from minimal input data.

Contribution

It presents a novel phase-amplitude reduction approach for system identification near Hopf bifurcations, applicable with limited pulse inputs and facilitating closed-loop control.

Findings

Effective model inference with as few as two pulse inputs

Application to circadian oscillation examples

Enabling nonlinear optimal control solutions

Abstract

A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase-amplitude reduction techniques, leveraging an analytical representation for the phase and amplitude response curves of the Hopf normal form to infer system parameters. Fitting can be performed by recording the system output during the relaxation to the stable limit cycle after applying as few as two carefully timed pulse inputs. This strategy is illustrated in two examples with relevance to circadian oscillations. In each example, the proposed model identification strategy allows for the formulation, solution, and implementation of a closed loop nonlinear optimal control problem.