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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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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Lower semicontinuity of attractors for non-autonomous dynamical systems [PDF]
, 2009 This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic
Langa, José A. +3 more
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Convergent normal forms of symmetric dynamical systems [PDF]
Journal of Physics A: Mathematical and General, 1997 It is shown that the presence of Lie-point-symmetries of (non-Hamiltonian) dynamical systems can ensure the convergence of the coordinate transformations which take the dynamical sytem (or vector field) into Poincaré-Dulac normal form.
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Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt
Abstract and Applied Analysis, 2014 This paper is concerned with the computation of the normal form and its application to a viscoelastic moving belt. First, a new computation method is proposed for significantly refining the normal forms for high-dimensional nonlinear systems.
S. P. Chen, Y. H. Qian
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An Algorithm for Computing a New Normal Form for Dynamical Systems
Journal of Symbolic Computation, 2000 Autonomous dynamical systems \(\dot{x}=F(x)\) are considered, with \(x\in \mathbb{R}^n\), \(F(x)\) is a vector whose components are formal power series and \(F(0)=0\). A new formal normal form for system (1) is proposed which improves the classical normal forms in the sense that it is a further reduction of the classical normal forms.
Guoting Chen, Jean Della Dora
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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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Polynomial and linearized normal forms for almost periodic differential systems [PDF]
, 2016 Agraïments: The first author is partially supported by NSFC key program of China (no. 11231001). The MINECO/FEDER grant UNAB13-4E-1604. And the third is supported by NSFC for Young Scientists of China (no.
Wu, Hao, Llibre, Jaume, Li, Weigu
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Some results on the dynamics generated by the Bazykin model
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2006 A predator-prey model formerly proposed by A. Bazykin et al. [Bifurcation diagrams of planar dynamical systems (1985)] is analyzed in the case when two of the four parameters are kept fixed.
Georgescu, R M, Georgescu, A
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