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
Hynne, F., Ipsen, M., Soerensen, P. G.
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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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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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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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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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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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Amplified Hopf bifurcations in feed-forward networks [PDF]
, 2012 In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with 2-dimensional cells. Our
Rink, Bob, Sanders, Jan
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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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Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations [PDF]
Mathematical Research Letters, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guysinsky, M., Katok, A.
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