Related papers: Response solutions for forced systems with large d…
We consider a class of differential equations, $\ddot x + \gamma \dot x + g(x) = f(\omega t)$, with $\omega \in {\bf R}^{d}$, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We…
We study the response of one dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system…
We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is relatively high or low. We show that, provided the…
We study the ordinary differential equation ${\varepsilon}\ddot x+\dot x + {\varepsilon} g(x) = {\varepsilon} f(\omega t)$, with $f$ and $g$ analytic and $f$ quasi-periodic in $t$ with frequency vector $\omega\in R^{d}$. We show that if…
We study the possibility of occurrence of vibrational resonance in a softening Duffing oscillator in the underdamped and overdamped cases both theoretically as well as numerically. The oscillator is driven by two periodic forces.…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
We establish the existence of quasi-periodic traveling wave solutions for the $\beta$-plane equation on $\mathbb{T}^2$ with a large quasi-periodic traveling wave external force. These solutions exhibit large sizes, which depend on the…
In this paper, we present an averaging method for obtaining quasi-periodic response solutions in perturbed, real analytic, quasi-periodic systems with Diophantine frequency vectors. Under the assumptions that the averaged system possesses a…
We give a simple proof of the existence of response solutions in some quasi-periodically forced systems with a degenerate fixed points. The same questions were answered in \cite{ss18} using two versions of KAM theory. Our method is based on…
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…
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…
This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at…
We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…
We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in…
This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to infinity, the dynamics reduces to that of a network under…
For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
We identify a class maximal dissipative solutions to models of compressible viscous fluids that maximize the energy dissipation rate. Then we show that any maximal dissipative solution approaches an equilibrium state for large times.
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…