Related papers: Forced Frequency Locking for Semilinear Dissipativ…
We study locking of the modulation frequency of a relative periodic orbit in a general $S^1$-equivariant system of ordinary differential equations under an external forcing of modulated wave type. Our main result describes the shape of the…
We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the…
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…
We study the behaviour of one-dimensional strongly dissipative systems subject to a quasi-periodic force. In particular we are interested in the existence of response solutions, that is quasi-periodic solutions having the same frequency…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…
We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of…
Solutions of a 1-D free-interface problem modeling solid combustion front propagating in combustible mixture with periodically varying concentration of reactant exhibit classical phenomenon of mode locking. Numerical simulation shows a…
We consider quasi-periodically systems in the presence of dissipation and study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term. When the dissipation is large enough and…
The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…
We consider boundary value problems for semilinear hyperbolic systems of the type $$ \partial_tu_j + a_j(x,\la)\partial_xu_j + b_j(x,\la,u) = 0, \; x\in(0,1), \;j=1,\dots,n $$ with smooth coefficient functions $a_j$ and $b_j$ such that…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
This paper concerns autonomous boundary value problems for 1D semilinear hyperbolic PDEs. For time-periodic classical solutions, which satisfy a certain non-resonance condition, we show the following: If the PDEs are continuous with respect…
A variant of the complex Ginzburg-Landau equation is used to investigate the frequency locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, $\pi$ fronts,…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
Using purely probabilistic methods, we prove the existence and the uniqueness of solutions fora system of coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous coefficients. As a…
Frequency locking to an external forcing frequency is a {well} known phenomenon. In the auditory system, it results in a localized traveling wave, the shape of which is essential for efficient discrimination between incoming frequencies. An…