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Data-Driven Bifurcation Analysis via Learning of Homeomorphism (2312.06634v1)
Published 11 Dec 2023 in eess.SY, cs.SY, and math.DS
Abstract: This work proposes a data-driven approach for bifurcation analysis in nonlinear systems when the governing differential equations are not available. Specifically, regularized regression with barrier terms is used to learn a homeomorphism that transforms the underlying system to a reference linear dynamics -- either an explicit reference model with desired qualitative behavior, or Koopman eigenfunctions that are identified from some system data under a reference parameter value. When such a homeomorphism fails to be constructed with low error, bifurcation phenomenon is detected. A case study is performed on a planar numerical example where a pitchfork bifurcation exists.
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