Estimating Critical Hopf Bifurcation Parameters for a Second-Order Delay Differential Equation with Application to Machine Tool Chatter

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Updated semi‐discretization method for periodic delay‐differential equations with discrete delay (2004, background): “Recently, the investigation of periodic motion of DDEs and the associated variational systems (that are time periodic DDEs) has come into the focus of interest [26–29].”
Calculating Centre Manifolds for Delay Differential Equations Using Maple (2009, unknown): “Some authors have performed the construction by hand, e.g., Faria and Magalhães (1995a,b); Gilsinn (2002); Guo and Huang (2003); Guo et al. (2004); Guo (2005); Jiang et al. (2006); Kalmár-Nagy et al. (1999, 2001); Liu and Yuan (2005); Nayfeh (2008); Orosz and Stépán (2004, 2006); Sri Namachchivaya…”
Order reduction of retarded nonlinear systems – the method of multiple scales versus center-manifold reduction (2008, methodology): “The normal form of the Hopf bifurcations of Equation (50) was constructed using the method of multiple scales by Nayfeh et al. [13] and Nayfeh [14] and using a combination of the centermanifold theorem and the method of normal forms by Kalm´ ar-Nagy et al. [23] and Gilsinn [ 24 ].”