Results 251 to 260 of about 12,042 (291)
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Normal Forms of Dynamical Systems and Bifurcations
2003We show the existence of a general class of bifurcating solutions to dynamical systems, by introducing their (Poincare-Dulac) normal form, and imposing that the normalizing transformation is convergent. These bifurcating solutions include standard stationary and Hopf bifurcations, and multiple-periodic solutions as well.
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A perturbation method for computing the simplest normal forms of dynamical systems
Journal of Sound and Vibration, 2003Abstract A previously developed perturbation method is generalized for computing the simplest normal form (at each level of computation, the minimum number of terms are retained) of general n -dimensional differential equations. This “direct” approach, combining the normal form theory with center manifold theory in one unified procedure, can be used
P. Yu, A.Y.T. Leung
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THE NORMAL FORMS, AVERAGING AND THE RESONANCE CONTROL OF NONLINEAR DYNAMICAL SYSTEMS
IFAC Proceedings Volumes, 1992Abstract The generalized normal forms and resonance control methodology is used to analyze and design efficient control of two generic mechanical systems. The first system represents a reduced model arising in nonlinear flexible- body dynamics, while the second describes an unstable regime of aircraft flight relevant to the saddle-node bifurcation ...
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On constrained dynamics and a pseudo-normal form for nonlinear systems
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 2002A nonlinear system in pseudo-normal form has the property that its family of linearizations about constant operating points specifies a family of linear systems in normal form. The purpose of this paper is to show that under certain assumptions a pseudo-normal form can be defined that has the following properties in common with the exact normal form: a
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Anticontrol of chaos for dynamic systems in p-normal form: A homogeneity-based approach
Chaos, Solitons & Fractals, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Ruoting +3 more
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Simultaneous local normal forms of dynamical systems with singular underlying geometric structures
NonlinearityInternational audienceAbstract The aim of this paper is to develop, for the first time, a general theory of simultaneous local normalisation of couples ( X , G ) , where X is a dynamical system (vector field) and G is an underlying geometric structure ...
Tudor S Raţiu, Nguyen Tien Zung
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Normal form solutions of dynamical systems in the basin of attraction of their fixed points
Physica D: Nonlinear Phenomena, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bountis, Tassos +2 more
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Improved Adjoint Operator Method and Normal Form of Nonlinear Dynamical System
Applied Mechanics and Materials, 2013An improved adjoint operator based on the adjoint operator concept of linear operator and S-N decomposition is proposed to calculate the normal forms of k order general nonlinear dynamic systems.Firstly, the whole polynomial solution space of homogeneous nilpotent partial differential equation are obtained.Secondly, the polynomial solution mentioned ...
Jun Jun Li, Xiao Qing Liu, Shi Zhu Yang
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Diffusive Stability of Turing Patterns via Normal Forms
, 2013We investigate dynamics near Turing patterns in reaction–diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a “normal form” coordinate system near such Turing patterns which exhibits an
A. Scheel, Qiliang Wu
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On the application of normal forms near attracting fixed points of dynamical systems
Physica A: Statistical Mechanics and its Applications, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bountis, Tassos, Tsarouhas, George
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