Center Manifold Analysis of the Delayed Lienard Equation

Application of the Liapunov–Floquet transformation to differential equations with time delay and periodic coefficients

“…The systems to which the proposed technique is applied in this paper are limited to linear homogeneous DDEs, therefore, the direct comparison of the proposed approach and the aforementioned techniques goes beyond the scope of this work. In particular, a comparison of the technique presented in this paper with those presented in previous publications (Kalma´r-Nagy et al 2001;Gilsinn 2002;Nayfeh 2008;Zhao and Kalma´r-Nagy 2009) is inadequate due to the lack of periodic coefficients in the systems considered in these works. In addition, the approach considered in this work is not limited to the analysis of system dynamics on a center manifold which makes it advantageous over other methods.…”

“…In fact, combining ChSCTA, LFT, and order reduction creates a new technique for the analysis of timeperiodic nonlinear DDEs which is an alternative to the existing techniques for dimensional reduction such as center manifold analysis of nonlinear constant (Kalma´r-Nagy et al 2001;Gilsinn 2002;Zhao and Kalma´r-Nagy 2009) and periodic nonlinear DDEs (Deshmukh et al 2008) and the multiple scales method (Nayfeh 2008) applied to nonlinear constant DDEs. The systems to which the proposed technique is applied in this paper are limited to linear homogeneous DDEs, therefore, the direct comparison of the proposed approach and the aforementioned techniques goes beyond the scope of this work.…”