Spectral submanifolds in time delay systems

Abstract The concept of spectral submanifolds, a powerful method of model order reduction of nonlinear systems, is extended to time delay systems that have infinite dimensional phase space representation. The proposed sun-star calculus based algorithm results in system reduction to manifolds which are constructed corresponding to either a real eigenvalue or to a pair of complex conjugate eigenvalues of the linearized system. Furthermore, it allows an improved approximation of self-excited oscillations exactly at the parameter point of interest, which could be further away from the corresponding Hopf bifurcation point. The paper includes case studies that demonstrate the capabilities of the algorithm.