P-Bifurcations in Stochastic Flutter Model Under Turbulence

TL;DR

This paper introduces a topology-based framework using persistent homology to detect stochastic bifurcations in aeroelastic systems under turbulence, providing a scalable method for analyzing complex stochastic dynamics.

Contribution

It presents a novel approach combining kernel density estimation and persistent homology to identify stochastic bifurcations in aeroelastic models with different turbulence excitations.

Findings

Homological bifurcation plots detect shifts in bifurcation onset.

Method reveals topological changes not evident in traditional analysis.

Framework is scalable and automatable for complex systems.

Abstract

Aeroelastic flutter represents a critical nonlinear instability arising from the coupling between structural elasticity and unsteady aerodynamics. In deterministic settings, flutter onset is associated with bifurcations of invariant sets such as equilibria or limit cycles. However, under stochastic excitation, long-time system behavior is better described in terms of stationary probability distributions rather than trajectory-based attractors. In this work, we present a topology-based framework to detect stochastic (P-)bifurcations in a two-degree-of-freedom aeroelastic system with structural nonlinearity. The method operates on high-dimensional stationary distributions reconstructed via kernel density estimation (KDE) and characterizes their structure using persistent homology. We compare bifurcation behavior across three excitation models: sinusoidal perturbations, Dryden turbulence, and von Karman turbulence. While conventional time-domain and phase-space analyses reveal only modest differences between these models, the proposed homological bifurcation plots detect consistent shifts in bifurcation onset and topological structure. The approach enables automated and scalable analysis of stochastic bifurcations in complex dynamical systems.