The Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling

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Calculating Centre Manifolds for Delay Differential Equations Using Maple (2009, unknown): “Perturbation techniques (multiple scales, Poincar´e-Lindstedt, averaging) have been used to study Hopf bifurcation by Campbell et al. (2006); Chow and Mallet-Paret (1977); Das and Chatterjee (2002); Gopalsamy and Leung (1996); Nayfeh (2008); Rand and Verdugo (2007); Stech (1979) and Wirkus and Rand”
Mathieu's Equation and Its Generalizations: Overview of Stability Charts and Their Features (2018, result): “as in many authors’ works (see, for example, Morrison and Rand [32], Atay [35], and Wirkus and Rand [36]), which results in the slow flow being ODEs rather than DDEs.”
2:1 Resonance in the delayed nonlinear Mathieu equation (2007, background): “In deriving Equation (A.8) the product eTcrit was assumed to be small [ 11 ].”
Eigenvalue Assignment via the Lambert W Function for Control of Time-delay Systems (2010, methodology): “…t h (30) Equations of this type were investigated using the asymptotic perturbation method (Maccari, 2001), bifurcation methods (Reddy et al., 2000 Wirkus and Rand, 2002 Xu and Chung, 2003) and the Taylor expansion with averaging (Li et al., 2006) to show that vibration control and quasi-periodic…”