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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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Lie point-symmetries and Poincare normal forms for dynamical systems
Journal of Physics A: Mathematical and General, 1990The problem of finding the extended Lie-point time-independent symmetries of autonomous systems of ordinary differential equations is compared with the Poincare procedure of reducing the system to linear or normal form, showing a close relationship between the two problems.
CICOGNA, GIAMPAOLO, Gaeta G.
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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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Normal form analysis of stochastically forced dynamical systems
Dynamics and Stability of Systems, 1986The possibility of reducing the dynamics of a system undergoing a Hopf bifurcation and forced by multiplicative noise to a universal normal form is examined on a simple model of geophysical interest. It is shown that the normal form equations and the stationary probability distribution depend on the way the noise is coupled to the original system.
Nicolis, Catherine, Nicolis, Grégoire
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Normal form of holomorphic dynamical systems
2008This article represents the expanded notes of my lectures at the ASI "Ham- iltonian Dynamical Systems and applications". We shall present various recent re- sults about normal forms of germs of holomorphic vector fields at a fixed point in C n . We shall explain how relevant it is for geometric as well as for dynamical pur- pose.
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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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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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Counter-Examples in Dynamical Systems via Normal Form Theory
SIAM Review, 1986The theory of normal forms is used to construct examples and counter- examples in the theory of ordinary differential equations. Selected examples from linearization theory, stability theory, bifurcation theory and theory of integrability are given ...
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On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems
American Journal of Mathematics, 1936Introduction. Let m be the number of degrees of freedom of a linear conservative dynamical systenm and let the point (q1, q2,9 * , q'Mn Pl p2, . . . p'mt) of the phase space be denoted by x = (xl, x2, , x.2M). A system of 2m ordinary differential equations of the first order, which are homogeneous, linear and do not contain t explicitly, is a canonical
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Analysis of non-linear dynamical systems by the normal form theory
Journal of Sound and Vibration, 1991A method is proposed for calculating the periodic solutions of non-linear mechanical systems with analytical non-linearities. The Jordan normalization procedure for the case of non-linear autonomous systems is described and generalized to dampened harmonically excited oscillators.
Jézéquel, Louis +1 more
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