Related papers: A Unified Floquet Theory for Discrete, Continuous,…
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on…
Floquet multipliers (characteristic multipliers) play significant role in the stability of the periodic equations. Based on the iterative method, we provide a unified algorithm to compute the Floquet multipliers (characteristic multipliers)…
Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with $T$-periodic coefficients, we can apply a, possibly complex,…
In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ As a corollary, the lower and upper bounds for the Floquet characteristic exponents are…
The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…
We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third…
Floquet theory, first published in 1883 for periodic linear differential equations, is extended in this paper to multitime diagonal recurrences. We find explicitly a monodromy matrix, and we comment its eigenvalues (called Floquet…
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider a linear system of differential equations with a time-periodic coefficient matrix. Assuming that the coefficient matrix depends…
The conventional characterization of periodically driven systems usually necessitates the time-domain information beyond Floquet bands, hence lacking universal and direct schemes of measuring Floquet topological invariants. Here we propose…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
A general theoretical framework for the study of electronic stopping of particle projectiles in crystalline solids is proposed. It neither relies on perturbative or linear response approximations, nor on an ideal metal host. Instead, it…
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
We consider a completely integrable system of differential equations in arbitrary dimensions whose phase space contains an open set foliated by periodic orbits. This research analyzes the persistence and stability of the periodic orbits…
The aim of our paper is to formulate and solve problems concerning linear multiple periodic recurrence equations. Among other things, we discuss in detail the cases with periodic and multi-periodic coefficients, highlighting in particular…
This work demonstrates that the Lyapunov method can effectively identify the growth rate of a linear time-periodic system describing cold fresh water on top of hot salty water with a periodically time-varying background shear flow. We…
We present a version of the classical Floquet-Lyapunov theorem for $\omega-$periodic nonautonomous linear (impulsive and non-impulsive) differential equations with piecewise constant arguments of generalized type (in short, IDEPCAG or…
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged…
Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around…
We propose an implementation of a method based on Fourier analysis to obtain the Floquet characteristic exponents for periodic homogeneous linear systems, which shows a high precision. This implementation uses a variational principle to…