Differentialgleichungen mit periodischen Koeffizienten: Floquet-Theorem

Physik Online ◽  
2018 ◽  
Author(s):  
Michael Bestehorn
Keyword(s):  
Floquet Theorem

scholarly journals Analyzing Glide-Symmetric Holey Metasurfaces Using a Generalized Floquet Theorem

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 71743-71750 ◽  
Author(s):  
Fatemeh Ghasemifard ◽  
Martin Norgren ◽  
Oscar Quevedo-Teruel ◽  
Guido Valerio
Keyword(s):  
Floquet Theorem

scholarly journals On the Study of Chemostat Model with Pulsed Input in a Polluted Environment

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Zhong Zhao ◽  
Xinyu Song
Keyword(s):  
Periodic Solution ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Polluted Environment ◽  
Chemostat Model ◽  
Globally Asymptotically Stable ◽  
Floquet Theorem

Chemostat model with pulsed input in a polluted environment is considered. By using the Floquet theorem, we find that the microorganism eradication periodic solution is globally asymptotically stable if the impulsive periodTis more than a critical value. At the same time, we can find that the nutrient and microorganism are permanent if the impulsive periodTis less than the critical value.

scholarly journals Bloch impedance analysis for a left handed transmission line

2012 ◽  
Vol 63 (5) ◽  
pp. 310-315 ◽  
Author(s):  
Cumali Sabah ◽  
Fabio Urbani ◽  
Savas Uckun
Keyword(s):  
Dispersion Relation ◽  
Transmission Line ◽  
Frequency Dependence ◽  
Impedance Analysis ◽  
Numerical Results ◽  
Matrix Formulation ◽  
Left Handed ◽  
Lumped Elements ◽  
Floquet Theorem

In this study, the dispersion relation and the frequency dependence of Bloch impedance in a left handed transmission line (LH-TL) is carried out using the F-matrix formulation and Bloch-Floquet theorem. The artificial LH-TL formed by periodic lumped elements is described and the F-matrix, dispersion relation and the Bloch impedance are formulated according to this description. Numerical results for lossless and lossy LH-TL are presented and discussed.

On Computation of Approximate Lyapunov-Perron Transformations

2019 ◽  
Author(s):  
Ashu Sharma ◽  
Subhash C. Sinha
Keyword(s):  
Periodic System ◽  
Floquet Theory ◽  
State Transition ◽  
Adjoint System ◽  
Picard Iteration ◽  
Symbolic Form ◽  
Equivalent Systems ◽  
P Transformations ◽  
Time Invariant ◽  
Floquet Theorem

Abstract Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with quasi-periodic coefficients. Application of Lyapunov-Perron (L-P) transformations to such systems produce dynamically equivalent systems in which the linear parts are time-invariant. In this work, a technique for the computation of approximate L-P transformations is suggested. First, a quasi-periodic system is replaced by a periodic system with a ‘suitable’ large principal period to which Floquet theory can be applied. Then, the state transition matrix (STM) of the periodic system is computed in the symbolic form using shifted Chebyshev polynomials and Picard iteration method. Finally, since the STM can be expressed in terms of a periodic matrix and a time-invariant matrix (Lyapunov-Floquet theorem), this factorization is utilized to compute approximate L-P transformations. A two-frequency quasi-periodic system is investigated using the proposed method and approximate L-P transformations are generated for stable, unstable and critical cases. These transformations are also inverted by defining the adjoint system to the periodic system. Unlike perturbation and averaging, the proposed technique is not restricted by the existence of a generating solution and a small parameter. Approximate L-P transformations can be utilized to design controllers using time-invariant methods and may also serve as a powerful tool in bifurcation studies of nonlinear quasi-periodic systems.

scholarly journals Floquet theorem with open systems and its applications

2016 ◽  
Vol 93 (3) ◽  
Author(s):  
C. M. Dai ◽  
Z. C. Shi ◽  
X. X. Yi
Keyword(s):  
Open Systems ◽  
Floquet Theorem

Interaction between P, S1 and S2 waves in multilayered periodic monoclinic media at low frequencies

2019 ◽  
Vol 220 (3) ◽  
pp. 1947-1955
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Wave Propagation ◽  
Seismic Data ◽  
Layered Medium ◽  
Anisotropic Media ◽  
Pass Band ◽  
Low Frequencies ◽  
Propagator Method ◽  
The Matrix ◽  
Floquet Theorem ◽  
Insight Into

SUMMARY Application of the Floquet theorem and the matrix propagator method reduces the problem of the plane wave propagation in a periodically layered anisotropic media, to analysis of the properties of stationary envelopes of different wave modes propagating up- and downwards. We analyse the interchanging of stop- and pass-bands and their structure at low frequencies for a periodically layered medium with monoclinic symmetry. The analysis shows the effect of interaction between P,S1 and S2 wave multipliers for stop- and pass-band structure and gives insight into the wave propagation in vertically heterogeneous anisotropic media which is important in modelling and interpretation of seismic data.

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