Related papers: Forced Frequency Locking for Semilinear Dissipativ…
The response of a passive mode-locking mechanism, where gain and spectral filtering are saturated with the energy and loss saturated with the power, is examined under the presence of higher order effects. These include third order…
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…
We present a theoretical analysis of phase separation in the presence of a spatially periodic forcing of wavenumber q traveling with a velocity v. By an analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model we find…
The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic…
Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…
The auditory system displays remarkable sensitivity and frequency discrimination, attributes shown to rely on an amplification process that involves a mechanical as well as a biochemical response. Models that display proximity to an…
The ac response of self-sustained current oscillations (SSCOs) in GaAs/AlAs superlattices (SLs) is derived based on the deformation of a limit cycle under an external ac driving force. Frequency locking into an integer fraction of the ac…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…
Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at…
The interactions between linear elastic waves and a nonlinear crack with finite compressibility are studied in the one-dimensional context. Numerical studies on a hyperbolic model of contact with sinusoidal forcing have shown that the mean…
We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has…
We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…
We investigate parametric autoresonance: a persisting phase locking which occurs when the driving frequency of a parametrically excited nonlinear oscillator slowly varies with time. In this regime, the resonant excitation is continuous and…
We show how pattern formation in Faraday waves may be manipulated by varying the harmonic content of the periodic forcing function. Our approach relies on the crucial influence of resonant triad interactions coupling pairs of critical…
We use symmetry considerations to investigate how damped modes affect pattern selection in multi-frequency forced Faraday waves. We classify and tabulate the most important damped modes and determine how the corresponding resonant triad…
Weakly damped mechanical systems under small periodic forcing tend to exhibit periodic response in a close vicinity of certain periodic orbits of their conservative limit. Specifically, amplitude frequency plots for the conservative limit…
We study quasi periodic and frequency locked states that can occur in a sinusoidally driven linear harmonic oscillator in the special relativistic regime. We show how the shift in natural frequency of the oscillator with increasing…
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…
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications…