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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Normal stability of slow manifolds in nearly periodic Hamiltonian systems [PDF]
Journal of Mathematics and Physics, 2021 M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid oscillations are ...
J. Burby, E. Hirvijoki
semanticscholar +1 more source
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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Ultradiscrete bifurcations for one dimensional dynamical systems [PDF]
, 2020 Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscretized equations.The ultradiscrete equations are derived from the normal forms of one-dimensional nonlinear differential equations,each of which has saddle-node ...
S. Ohmori, Y. Yamazaki
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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 form transforms separate slow and fast modes in stochastic dynamical systems [PDF]
, 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 ...
Roberts, A. +2 more
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Resonances in a spring-pendulum: algorithms for equivariant singularity theory [PDF]
, 1998 A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained.
Vegter, G +15 more
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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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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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Resonant response functions for nonlinear oscillators with polynomial type nonlinearities [PDF]
, 2013 In this paper we consider the steady-state response of forced, damped, weakly nonlinear oscillators with polynomial type nonlinearities. In particular we define general expressions that can be used to compute resonant response functions which define the ...
Neild, S.A. +7 more
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