Normal Form Transforms Separate Slow and Fast Modes in Stochastic Dynamical Systems [PDF]
Physica A: Statistical Mechanics and Its Applications, 2008 © 2007 Elsevier B.V. All rights reserved.Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from insignificant detailed microscale ...
A J Roberts
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Geometry of Normal Forms for Dynamical Systems [PDF]
, 2018 We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting based on the action of certain groups.
Giuseppe Gaeta
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Observavility Brunovsky normal form: Multi-output linear dynamical systems [PDF]
2009 American Control Conference, 2009 This paper gives the sufficient and necessary conditions to guarantee the existence of a linear change of coordinates to transform a multi-output linear dynamical system (modulo a nonlinear term depending on inputs and outputs) in the observability Brunovsky canonical form.
Boutat, Driss +2 more
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Systematic derivation of amplitude equations and normal forms for dynamical systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1998 We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from ...
Ipsen, M. +2 more
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Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems [PDF]
Physica D: Nonlinear Phenomena, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Di Bernardo, M, Budd, C, Champneys, AR
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Formal equivalence between normal forms of reversible and hamiltonian dynamical systems
Communications on Pure and Applied Analysis, 2014 We show the existence of formal equivalences between reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.
Ricardo Miranda Martins
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Communications in Contemporary MathematicsIn this work, dynamical properties of the solutions of differential systems in the plane are provided using certain constants related with the Kowalevskaya exponents. An orbital normal form that allows to study the existence of analytic and non-analytic first integrals is given.
Antonio Algaba +3 more
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An upper bound for validity limits of asymptotic analytical approaches based on normal form theory [PDF]
, 2012 Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched.
LAMARQUE, Claude-Henri +2 more
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Unique normal forms near a degenerate elliptic fixed point in two-parametric families of area-preserving maps [PDF]
, 2014 We derive simplified normal forms for an area-preserving map in a neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points appear in generic families of area-preserving maps. We also derive a simplified normal form for a generic two-
Gelfreikh, Natalia, Gelfreich, Vassili
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Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator [PDF]
, 2014 This paper considers the dynamic response of coupled, forced and lightly damped nonlinear oscillators with two degree-of-freedom. For these systems, backbone curves define the resonant peaks in the frequency-displacement plane and give valuable ...
Neild, S.A. +6 more
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