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The center problem via averaging method
Journal of Mathematical Analysis and Applications, 2009 The averaging method has been used to study the problem of the determination of the number of hyperbolic limit cycles that can bifurcate from the period annulus of a center.
Isaac A Garcia, Jaume Gine
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Averaging method of granular materials
Physical Review E, 2002This paper presents an averaging method to link discrete to continuum variables of granular materials. Compared to the other methods proposed in the literature, it has advantages of being applicable to all flow regimes, and to granular flows with or without the effect of physical boundaries.
H P, Zhu, A B, Yu
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More on the Airy Averaging Method
Journal of Mathematical Chemistry, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
ARRIGHINI G. P. +2 more
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Periodic Solutions; Averaging Methods
1999Abstract Consider an equation of the form x εh(x, x) x 0 where ε is small. Such an equation is in a sense close to the simple harmonic equation x x 0, whose phase diagram consists of circles centred on the origin. It should be possible to take advantage of this fact to construct approximate solutions: the phase paths will be nearly ...
D W Jordan, P Smith
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1990
In this chapter we shall consider again equations containing a small parameter e. The approximation method leads generally to asymptotic series as opposed to the convergent series studied in the preceding chapter; see section 9.2 for the basic concepts and more discussion in Sanders and Verhulst (1985), chapter 2.
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In this chapter we shall consider again equations containing a small parameter e. The approximation method leads generally to asymptotic series as opposed to the convergent series studied in the preceding chapter; see section 9.2 for the basic concepts and more discussion in Sanders and Verhulst (1985), chapter 2.
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IRE Transactions on Circuit Theory, 1960
The method of averaging of van der Pol was devised to obtain periodic and almost periodic solutions of quasi-linear systems of differential equations. A theorem is stated for a particular case where this method has been justified mathematically and an example is given to illustrate the results.
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The method of averaging of van der Pol was devised to obtain periodic and almost periodic solutions of quasi-linear systems of differential equations. A theorem is stated for a particular case where this method has been justified mathematically and an example is given to illustrate the results.
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2003
Consider a weakly nonlinear oscillation problem $$ \ddot{x} + \varepsilon h(x,\dot{x}) + x = 0,{\text{ }}\varepsilon {\text{ < < 1}}{\text{.}} $$ (4.1.1)
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Consider a weakly nonlinear oscillation problem $$ \ddot{x} + \varepsilon h(x,\dot{x}) + x = 0,{\text{ }}\varepsilon {\text{ < < 1}}{\text{.}} $$ (4.1.1)
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1993
Regular perturbation methods are based on Taylor’s formula and on implicit function theorems. However, there are many problems to which Taylor’s formula cannot be applied directly, in which case perturbation methods based on multiple time or space scales can often be used, sometimes even for chaotic systems.
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Regular perturbation methods are based on Taylor’s formula and on implicit function theorems. However, there are many problems to which Taylor’s formula cannot be applied directly, in which case perturbation methods based on multiple time or space scales can often be used, sometimes even for chaotic systems.
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1976
In this paper we present several new aspects of the method of averages: first we describe some formal properties of the method, second we apply it in order to reprove Hopf’s bifurcation theorem (and obtain a direction of bifurcation formula which is similar to that of Hsu and Kazarinoff), thirdly we offer a theorem concerning error bounds.
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In this paper we present several new aspects of the method of averages: first we describe some formal properties of the method, second we apply it in order to reprove Hopf’s bifurcation theorem (and obtain a direction of bifurcation formula which is similar to that of Hsu and Kazarinoff), thirdly we offer a theorem concerning error bounds.
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Complexification-averaging method via the averaged Lagrangian
Nonlinear Dynamics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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