Normal forms for periodic systems

Polynomial and Linearized Normal Forms for Almost Periodic Differential Systems

For almost periodic differential systems ẋ = εf(x, t, ε) with x ∈ Cn, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neighborhood of a hyperbolic singular point of the system ẋ = ε limT→∞ 1 T ∫ T 0 f(x, t, 0) dt, if its eigenvalues are in the Poincaré domain. The normal form linearizes if the real part of the eigenvalues are non–resonant.

Carleman linearization and normal forms for differential systems with quasi-periodic coefficients

We study the matrix representation of Poincaré normalization using the Carleman linearization technique for non-autonomous differential systems with quasi-periodic coefficients. We provide a rigorous proof of the validity of the matrix representation of the normalization and obtain a recursive algorithm for computing the normalizing transformation and the normal form of the differential systems...

Normal Forms for Coupled Takens-Bogdanov Systems

The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis for the ideal of relations and a Stanley decomposition for the ring of invariants that arise...

Normal forms for spiking neural P systems

1 Department of Computer Science University of California Santa Barbara, CA 93106, USA [email protected], [email protected] 2 Department of Computer Science, Louisiana Tech University, Ruston PO Box 10348, Louisiana, LA-71272 USA [email protected] 3 Universidad Politécnica de Madrid UPM, Faculdad de Informática Campus de Montegancedo s/n, Boadilla del Monte, 28660 Madrid, Spain [email protected]...

Two Normal Forms for Rewriting P Systems