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   Articles with "normal forms" as a keyword



Observer normal forms for a class of nonlinear systems by means of coupled auxiliary dynamics

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recommendations! Published in 2020 at "International Journal of Robust and Nonlinear Control"

DOI: 10.1002/rnc.5027

Abstract: This work aims at developing a class of nonlinear dynamical systems that can be converted into nonlinear observer normal forms, which support the well‐known high gain observer. This will be performed by means of the… read more here.

Keywords: auxiliary dynamics; dynamical systems; observer normal; class nonlinear ... See more keywords
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Convergence to Normal Forms of Integrable PDEs

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recommendations! Published in 2019 at "Communications in Mathematical Physics"

DOI: 10.1007/s00220-019-03661-8

Abstract: In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can… read more here.

Keywords: integrable pdes; convergence normal; normal form; forms integrable ... See more keywords
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Normal forms for rank two linear irregular differential equations and moduli spaces

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recommendations! Published in 2021 at "Periodica Mathematica Hungarica"

DOI: 10.1007/s10998-021-00408-8

Abstract: We provide a unique normal form for rank two irregular connections on the Riemann sphere. In fact, we provide a birational model where we introduce apparent singular points and where the bundle has a fixed… read more here.

Keywords: linear irregular; irregular differential; rank two; forms rank ... See more keywords
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Normal forms of C∞ vector fields based on the renormalization group

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recommendations! Published in 2021 at "Journal of Mathematical Physics"

DOI: 10.1063/5.0031043

Abstract: The normal form theory for polynomial vector fields is extended to those for C∞ vector fields vanishing at the origin. Explicit formulas for the C∞ normal form and the near identity transformation that brings a… read more here.

Keywords: normal forms; renormalization group; vector fields; normal form ... See more keywords

Orbital and parametric normal forms for families of Hopf-zero singularity

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recommendations! Published in 2024 at "Nonlinearity"

DOI: 10.1088/1361-6544/ad7662

Abstract: This paper explores the simplest truncated orbital and parametric normal forms of controlled Hopf zero singularities. We assume a quadratic generic condition and complete the remaining results on their simplest truncated orbital and parametric normal… read more here.

Keywords: families hopf; normal forms; forms families; parametric normal ... See more keywords

Local Integrability of Poincaré–Dulac Normal Forms

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recommendations! Published in 2018 at "Regular and Chaotic Dynamics"

DOI: 10.1134/s1560354718070080

Abstract: We consider dynamical systems in Poincaré–Dulac normal form having an equilibrium at the origin, and give a sufficient condition for them to be integrable, and prove that it is necessary for their special integrability under… read more here.

Keywords: local integrability; poincar dulac; dulac normal; normal forms ... See more keywords

SECOND-ORDER NORMAL FORMS FOR N-DIMENSIONAL SYSTEMS WITH A NILPOTENT POINT

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recommendations! Published in 2020 at "Journal of Applied Analysis and Computation"

DOI: 10.11948/20190393

Abstract: Normal forms theory is one of the most powerful tools for the study of nonlinear differential equations, in particular, for stability and bifurcation analysis. Many works paid attention to normal forms associated with nilpotent Jacobian… read more here.

Keywords: second order; complementary spaces; forms dimensional; order normal ... See more keywords