On Polynomial Forms Of Nonlinear Functional Differential Equations
JOURNAL OF COMPUTATIONAL DYNAMICS(2021)
摘要
In this paper we study nonlinear autonomous retarded functional differential equations; that is, functional equations where the time derivative may depend on the past values of the variables. When the nonlinearities in such equations are comprised of elementary functions, we give a constructive proof of the existence of an embedding of the original coordinates yielding a polynomial differential equation. This embedding is a topological conjugacy between the semi-flow of the original differential equation and the semi-flow of the auxiliary polynomial differential equation. Further dynamical features are investigated; notably, for an equilibrium or a periodic orbit and its embedded counterpart, the stable and unstable eigenvalues have the same algebraic and geometric multiplicity.
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关键词
Functional differential equations, automatic differentiation, equilibria, periodic orbits, invariant manifolds
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