# Floquet theorem

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## Floquet theorem

[flō′kā ‚thir·əm]
(mathematics)
A second-order linear differential equation whose coefficients are periodic single-valued functions of an independent variable x has a solution of the form e μ x P (x) where μ is a constant and P (x) a periodic function.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The study of differential equations with a periodic function in the differential operator is called Floquet Theory. Adopting this name, we refer to a quench that is periodic in time as Floquet quench.
Subjects such as existence and uniqueness of solutions, stability, Floquet theory, periodicity, stability, and boundedness of solutions can be studied more precisely and generally by utilizing dynamical systems on time scales.
Sorzia applies the Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide.
[20-22] presented the well-accepted semidiscretization methods (0st SDM and 1st SDM) based on Floquet theory for periodic delayed systems.
Propagation constant of CRLH-TL is determined by applying the periodic boundary conditions related to Bloch and Floquet theory. The CRLH TL unit cell's dispersion is obtained by:
According to Floquet theory, a periodic solution is stable when [absolute value of ([[rho].sub.j]) < 1 for each [[rho].sub.j] (except [[rho].sub.j] = 1).
Section 2 will review the effect of impulsive perturbations, establish conditions for extinction, and obtain the conditions for permanence of System (2) using the Floquet theory of impulsive equations at small-amplitude perturbation scales.
Figure 3 shows the predicted frequency response of Unit Cell I based on the Floquet theory and the simulation result of an ideal Salisbury screen for comparison.
A., "Floquet theory for partial differential equations," Russian Mathematical Surveys, Vol.
of Dayton, Ohio) introduce students and researchers to various spectral computational techniques, including k-space theory, Floquet theory, transfer matrix method, and beam propagation methods.
DaCunha, Lyapunov stability and Floquet theory for nonautonomous linear dynamic systems on time scales, PhD dissertation, (2004), Baylor University.
Multi-term equations and the Floquet theory. In this section we develop similar results to those of the previous section for multi-term equations of the form (1.1).
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