Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, methodology): “This is an important generalization, since it is now possible to identify a normal form from data, allowing for the prediction of bifurcation phenomena and dynamic unfoldings [2].”
Calculating Centre Manifolds for Delay Differential Equations Using Maple (2009, unknown): “For a general outline of this approach and some specific examples for ordinary differential equations see ( Guckenheimer and Holmes, 1983, p. 134 ) or (Wiggins, 1990, p. 198).”
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006, methodology): “We call such a model, containing the smallest number of variables and parameters that exhibits a behavior of interest, a template [131].”
Data-driven discovery of coordinates and governing equations (2019, background): “The choice of basis functions typically reflects some knowledge about the system of interest: a common choice is polynomials in x as these are elements of many canonical models of dynamical systems [48].”
Equation-free: The computer-aided analysis of complex multiscale systems (2004, background): “A direct conceptual analogy arises with center manifolds in dynamical systems (parameterized using eigenvectors of the linearization, Guckenheimer and Holmes, 1983), or inertial manifolds for dissipative PDEs (Constantin et al., 1988; Temam, 1990).”