Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

摘要: We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments such equations, many authors recommend a center manifold reduction as first step. demonstrate that the method multiple scales, on simply discarding infinitely exponentially decaying components complementary solutions obtained at each stage approximation, can bypass explicit calculation. Analytical approximations for DDEs studied closely match numerical solutions.