Periodic Center Manifolds for DDEs in the Light of Suns and Stars

Abstract

In this paper we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay differential equations by using the Lyapunov-Perron method. The results are based on the rigorous functional analytic perturbation framework for dual semigroups (sun-star calculus). The generality of the dual perturbation framework shows that the results extend to a much broader class of evolution equations.

41 pages

References in corpus (3)

• Neural Field Models with Transmission Delays and Diffusion
• Dynamics of delayed neural field models in two-dimensional spatial domains
• Bifurcations of Neural Fields on the Sphere

Cited by in corpus (2)

• Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs
• Periodic Normal Forms for Bifurcations of Limit Cycles in DDEs