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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Dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамика, 2023 The subject of this work is the study of local dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings. From a discrete model describing the dynamics of a great number of coupled oscillators, a transition has been
Kashchenko, Sergej Aleksandrovich
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Geometry and integrability of quadratic systems with invariant hyperbolas
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Let QSH be the family of non-degenerate planar quadratic differential systems possessing an invariant hyperbola. We study this class from the viewpoint of integrability.
Regilene Oliveira +2 more
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Normal forms, symmetry and linearization of dynamical systems [PDF]
Journal of Physics A: Mathematical and General, 1998 19 pages, no ...
Dario Bambusi +3 more
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Bursting Dynamics in a Singular Vector Field with Codimension Three Triple Zero Bifurcation
Mathematics, 2023 As a kind of dynamical system with a particular nonlinear structure, a multi-time scale nonlinear system is one of the essential directions of the current development of nonlinear dynamics theory.
Weipeng Lyu +3 more
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Bifurcations of dynamical systems with sliding: derivation of normal-form mappings [PDF]
Physica D: Nonlinear Phenomena, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DI BERNARDO, MARIO +2 more
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Nonlinear Modal Decoupling of Multi-Oscillator Systems With Applications to Power Systems
IEEE Access, 2018 Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such systems, we propose a nonlinear modal decoupling (NMD) approach inversely constructing as many ...
Bin Wang, Kai Sun, Wei Kang
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Further Reductions of Normal Forms for Dynamical Systems
Journal of Differential Equations, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Guoting, Della Dora, Jean
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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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