Equivariant Hopf bifurcation for neutral functional differential equations

By Shangjiang Guo, Jeroen S. W. Lamb. 2008

46 citations recorded by the source corpus.

In this paper we employ an equivariant Lyapunov-Schmidt procedure to give a clearer understanding of the one-to-one correspondence of the periodic solutions of a system of neutral functional differential equations with the zeros of the reduced bifurcation map, and then set up equivariant Hopf bifurcation theory. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction.

Subfields: Computer Networks and Communications, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fef313b1a05a875626f255caeb5db75ea5f08753

Citations in the corpus

• Global Hopf bifurcation for differential equations with state-dependent delay (2010, unknown): “Our global bifurcation theory is, in principle, applicable to general system of FDEs with state-dependent delay and even some neutral equations with appropriate further development (see [15] for some work on equivalent local Hopf bifurcations of neutral equations with constant delays).”