Normal forms for retarded functional differential equations associated with zero-double-Hopf singularity with $1:1$ resonance - Houssem Achouri (Electronic Journal of Qualitative Theory of Differential Equations)
This manuscript introduces a framework that focuses on the singularity of a zero-double-Hopf system with $1:1$ resonance in general retarded differential equations (RDDs). Initially, practical algorithms are proposed to identify the zero-double-Hopf singularity and the associated generalized eigenspace that corresponds to zero and two pairs of purely imaginary eigenvalues. Subsequently, by utilizing center manifold reduction and normal form techniques, we derive a reduced form of parameterized retarded differential systems up to third-order terms.