We consider a T-periodically perturbed autonomous functional differential equation of neutral type. We assume the existence of a T-periodic limit cycle x_0 for the unperturbed autonomous system. We also assume that the linearized unperturbed equation around the limit cycle has the characteristic multiplier 1 of geometric multiplicity 1 and algebraic multiplicity greater than 1. The paper deals with the existence of a branch of T-periodic solutions emanating from the limit cycle.
Couchouron, J.-., Kamenskiǐ, M., Mikhaylenko, B., Nistri, P. (2015). Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 46(2), 631-663 [10.12775/TMNA.2015.062].
Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case
Nistri, P.
2015-01-01
Abstract
We consider a T-periodically perturbed autonomous functional differential equation of neutral type. We assume the existence of a T-periodic limit cycle x_0 for the unperturbed autonomous system. We also assume that the linearized unperturbed equation around the limit cycle has the characteristic multiplier 1 of geometric multiplicity 1 and algebraic multiplicity greater than 1. The paper deals with the existence of a branch of T-periodic solutions emanating from the limit cycle.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/48455