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Monday, July 27, 2020 | History

2 edition of computation and use of Floquet multipliers for bifurcation analysis. found in the catalog.

computation and use of Floquet multipliers for bifurcation analysis.

Thomas Frederick Fairgrieve

computation and use of Floquet multipliers for bifurcation analysis.

by Thomas Frederick Fairgrieve

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  • 25 Currently reading

Published .
Written in English


The Physical Object
Pagination110 leaves.
Number of Pages110
ID Numbers
Open LibraryOL16423624M
ISBN 100315926228

In this paper, a new analysis technique in the study of dynamical systems with periodically varying parameters is presented. The method is based on the fact that all linear periodic systems can be replaced by similar linear time-invariant systems through a suitable periodic transformation known as the Liapunov-Floquet (L-F) :// /Liapunov-Floquet-Transformation-Computation-and. In this paper we investigate collocation methods for the computation of periodic solutions of autonomous delay differential equations (DDEs). Periodic solutions are found by solving a periodic two-point boundary value problem, which is an infinite-dimensional problem for DDEs, in contrast to the case of ordinary differential ?cid=

The paper presents a critical discussion of the electro-thermal instability in multifinger HBTs based on Floquet Multipliers analysis. We show that the usual interpretation of current collapse as a bifurcation phenomenon for layouts with more than two fingers strictly holds only if inter-finger thermal coupling is neglected. Thus, predictive criteria based on the identification of singularity   convergence, but we refrain from a genuine convergence analysis. In some cases (demos cgl in 3D and brussel in 2D, and cgldisk, gksspirals) we additionally switch o the on the y computation of Floquet multipliers and instead compute the multipliers a posteriori at selected points on ://

  This chapter demonstrates analysis and control of the attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit. The attitude motion is modeled by nonlinear planar pitch dynamics with periodic coefficients and additionally subjected to external periodic excitation. Consequently, using system state augmentation, Lyapunov-Floquet (L-F) transformation, and normal form   More specifically, we use numerical bifurcation analysis tools to explore directly regions of delay-induced resonances and other stability boundaries in this delay-differential equation model for ENSO. Keywords: delay differential equations, they are all stable, as was checked with the computation of the Floquet multipliers (not shown).


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Computation and use of Floquet multipliers for bifurcation analysis by Thomas Frederick Fairgrieve Download PDF EPUB FB2

In the determination of the asymptotic stability and bifurcation behaviour of periodic orbits it is necessary to accurately compute the Floquet multipliers having modulus nearly 1 and to determine the number of multipliers that lie well inside and well outside the unit ://   This paper studies numerical methods for linear stability analysis of periodic solutions in codes for bifurcation analysis of small systems of ordinary differential equations (ODEs).

Popular techniques in use today (including the AUTO97 method) produce very inaccurate Floquet multipliers if the system has very large or small :// Therefore we can use the ideas behind the Newton--Picard method developed for the computation of periodic solutions of dissipative systems of PDEs [Roose et al., ; Lust et al., ].

This algorithm can compute branches of periodic solutions and at little extra cost also the dominant, stability-determining Floquet ?doi=    IEICE TRANS. FUNDAMENTALS, VOL.E92–A, NO.5 MAY Fig.1 The Floquet multipliers λ j (j =1,2) computed with the conven- tional method “Method 1” for the Mathieu equations (7).

p: the parameter of the equations. Suitable choice of the initial condition X 0(0) reduces errors of numerical computation of eigenvalues of X 0(T), namely, Floquet ://   In the determination of the asymptotic stability and bifurcation behaviour of periodic orbits it is necessary to accurately compute the Floquet multipliers having modulus nearly 1 and to determine the number of multipliers that lie well inside and well outside the unit circle.

Current numerical methods for computing Floquet multipliers suffer a loss of accuracy in two cases of importance ?mobileUi=0. Lust K., Roose D.

() Computation and Bifurcation Analysis of Periodic Solutions of Large-Scale Systems. In: Doedel E., Tuckerman L.S. (eds) Numerical Methods for Bifurcation Problems and Large-Scale Dynamical :// We consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous ODEs, namely the fold, the period-doubling (or flip) bifurcation, and the torus (or Neimark–Sacker) bifurcation.

The Computations and Use of Floquet Multipliers for Bifurcation Analysis, Ph.D   Computation and bifurcation analysis of periodic solutions of large-scale systems_专业资料 84 All Floquet multipliers larger than in modulus were also computed.

In the region with chaotic dynamics, one of the Floquet multipliers grows to values around  › 百度文库 › 互联网. Computation of Floquet Multipliers Using an Iterative Method for Variational Equations Article in IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences A(5   through the Floquet multipliers.

However, the resolution of the extra equation with the secant method makes the implementation inefficient when the size of the system increases. In this context, the main contribution of the present paper is to adapt classical tools for bifurcation analysis in codimension-2 parameter space to the HB formalism   Embedding harmonic balance results in Floquet theory, an approach for locating the characteristic multipliers is developed.

The resulting technique, based on a first order approximation, analyses the loss of stability of the limit cycles and gives effective conditions for the prediction of cyclic fold, flip and Neimark-Sacker bifurcation ://   bifurcations from periodic orbits, and to trace bifurcation curves in parameter space, by computing the Floquet multipliers of the periodic orbits.

In this direction, see in particu-lar [45,52,56,77] for impressive results in fluid problems. 1Originally, pde2path was based on the Matlab pdetoolbox, with d =2. Then, as also detailed in   Tom Fairgrieve, The Computation and Use of Floquet Multipliers for Bifurcation Analysis, Jan.

Currently a Senior Lecturer in the Department of Computer Science, University of Toronto. David Fleet, Measurement of Image Velocity, Jan. Currently a Professor in the Department of Computer Science, University of ~jepson/ Koen Engelborghs Tatyana Luzyanina, Giovanni Samaey, Dirk Roose, Koen VerheydenDepartment of Computer Science Celestijnenlaan A B Leuven Belgium Functionality: DDE-BIFTOOL is a Matlab package for numerical bifurcation and stability analysis of delay differential equations with several fixed discrete and/or state-dependent AUTO determines the characteristic multipliers (or Floquet multipliers), that reflect asymptotic stability and bifurcation properties, as a by-product of the decomposition of the Jacobian of the Abstract.

We present analytical and numerical results about Floquet multipliers of special symmetric solutions of differential delay equations. We describe numerical procedures for the calculation of Poincaré maps, and we report experimental observations on bifurcations; in particular, period Bifurcation and local stability analysis of the nonlinear parametric pendulum of.

(a) First and second parametric resonances showing the amplitudes of harmonics 1/2 and 1 of θ(t) as a function of ω. (b) Locus of the Floquet multipliers in the complex plane for the trivial branch θ(t)=0 when ω   At λ ≈this complex pair of critical Floquet exponents become real and negative, thus corresponding to negative real Floquet multipliers as described in section 4.

We follow the interesting real Floquet exponent in the third graph of Figure 8, this time plotting it against  › 百度文库 › 互联网. automatically because the computation of eigenvalues or Floquet multipliers may require more computational effort than the computation of the equilibria or periodic orbits (for example, if the d We describe the algorithms used in the Matlab continuation and bifurcation package pde2path for Hopf bifurcation and continuation of branches of periodic orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the computation of Floquet multipliers.

We first test the methods on three reaction diffusion examples, namely a complex Ginzburg-Landau equation as a toy problem, a. automatically because the computation of eigenvalues or Floquet multipliers may require more computational effort than the computation of the equilibria or periodic orbits (for example, if the system dimension is small but one delay is large)?doi=&rep=rep1&type=pdf.

MRI Master Class / Numerical Bifurcation Analysis of Dynamical Systems Poincaré maps and Floquet multipliers-- Centre Manifold and Normal Form reduction A reference book would be Stephen P. Ellner and J. Guckenheimer, Dynamic models in ~kouzn/  solutions and their dominant Floquet multipliers.

Section 3 presents defin-ing systems for codimension-one bifurcations of periodic solutions that allow one to compute the location of bifurcation points accurately. Computation of connecting orbits is discussed in Sec. 4 and of quasiperiodic solutions is discussed in Sec. ://~kouzn/