Nonlinear Dynamics

, Volume 93, Issue 1, pp 63–78 | Cite as

Forecasting bifurcations of multi-degree-of-freedom nonlinear systems with parametric resonance

  • Shiyang Chen
  • Bogdan Epureanu
Original Paper


The location of bifurcation points and bifurcation diagrams is important for the understanding of a nonlinear system with parametric resonance. This paper presents a model-less method to predict bifurcations of slightly damped multi-degree-of-freedom nonlinear systems with parametric resonance using transient recovery data in the pre-bifurcation regime. This method is based on the observation that the envelope amplitude of a decaying response in the pre-bifurcation regime recovers more slowly to the equilibrium as the system becomes closer to the bifurcation. Data obtained from both simulations and experiments are used to forecast the location of the bifurcation point and the bifurcation diagram. Forecasting results demonstrate that the method can be used to predict the bifurcation accurately under a set of specific assumptions.


Parametric resonance Forecasting bifurcations Model-less approach 



This research was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number U01GM110744. The content is solely the responsibility of the authors and does not necessarily reflect the official views of the National Institutes of Health.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA

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