Explicit computational formulas for critical normal form coefficients of all codimension-one bifurcations of limit cycles in DDEs are derived and implemented numerically using a characteristic operator.
A class of abstract delay differential equations in the light of suns and stars
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abstract
Using dual perturbation theory in a non-sun-reflexive context, we establish a correspondence between 1. a class of nonlinear abstract delay differential equations (DDEs) with unbounded linear part and an unknown taking values in an arbitrary Banach space and 2. a class of abstract weak* integral equations of convolution type involving the sun-star adjoint of a translation-like strongly continuous semigroup. For this purpose we also characterize the sun dual of the underlying state space. More generally we consider bounded linear perturbations of an arbitrary strongly continuous semigroup and we comment on some implications for the particular case of abstract DDEs.
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Numerical Periodic Normalization at Codim 1 Bifurcations of Limit Cycles in DDEs
Explicit computational formulas for critical normal form coefficients of all codimension-one bifurcations of limit cycles in DDEs are derived and implemented numerically using a characteristic operator.