On the stability bifurcation of a nonlinear time delay system (Q1129639)

The authors consider the stability problem for nonlinear time delay systems. They use a center manifold approach in order to investigate the stability of trivial and nontrivial solutions to some equations studied earlier by \textit{J. Bentsman, K. S. Hong} and \textit{J. Fakhfakh} [Automatica 27, No. 3, 491-500 (1991; Zbl 0754.93065)]. The investigation of Hopf bifurcation of the nonlinear delay equation with fixed delay can be reduced to the study of a system of two ODEs. Explicit bifurcation equations are derived using a first approximation of the integral averaging method. Stability and instability regions are identified.