Data-driven bifurcation analysis using parameter-dependent trajectories

Abstract

Identification of bifurcation diagrams in nonlinear systems is of great importance for resilient design and stability analysis of dynamical systems. Data-driven identification of bifurcation diagrams has a significant advantage for large dimensional systems where analysis of the equations is not possible, and for experimental systems where accurate system equations are not available. In this work, a novel forecasting approach to predict bifurcation diagrams in nonlinear systems is presented using system trajectories before instabilities occur. Unlike previous techniques, the proposed method considers a varying bifurcation parameter during the system response to perturbations. Combined with an asymptotic analysis provided by the method of multiple scales eliminates the requirement of using multiple measurements and allows the novel technique to predict the bifurcation diagram using a single system recovery. The proposed approach allows stability analyses of nonlinear systems with limited access to experimental or surrogate data. The novel technique is demonstrated through its application to a Hopf bifurcation, highlighting its inherent advantages. Subsequently, the method is employed in the analysis of an aeroelastic system that shows both supercritical and subcritical Hopf bifurcations. The findings reveal great accuracy, achieved with a reduced number of measurements, while enhancing versatility.