Normal form of double-Hopf singularity with 1:1 resonance for delayed differential equations - Wu, Xiaoqin P. P.; Wang, Liancheng (Nonlinear Analysis: Modelling and Control, 2019)
In this manuscript, we provide a framework for the double-Hopf singularity with 1:1 resonance for general delayed differential equations (DDEs). The corresponding normal form up to the third-order terms is derived. As an application of our framework, a double-Hopf singularity with 1:1 resonance for a van der Pol oscillator with delayed feedback is investigated to illustrate the theoretical results.