Related papers: System of nonlinear oscillators with dissipation. …
The mixed initial-boundary value problem for infinite one-dimensional chain of harmonic oscillators on the half-line is considered. We study the large time behavior of solutions and derive the dispersive bounds.
We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
In order to investigate the size limit on spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator…
In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the…
It is analytically shown that symmetry breaking, in dissipative systems, affects the nature of the bifurcation at onset of instability resulting in transitions from super to subcritical bifurcations. In the case of a nonlinear fiber cavity,…
We study an asymptotic behaviour of parametric autoresonance for non-linear equation. Main result of this work is statement about asymptotic behaviour of measure for captured trajectories. To find this we obtain an asymptotic expansion for…
The response of a large array of coupled nonlinear oscillators to parametric excitation is studied, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS).…
We discover presence of a hitherto unexplored type of resonance in a parametrically excited Van der Pol oscillator. The oscillator also possesses a state of anti-resonance. In the weak non-linear limit, we explain how to practically get a…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…
In this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with…
Nonlinearity induced nonreciprocity is studied in a system comprising two resonators coupled to a one-dimensional waveguide when the linear system does not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the coupled…
Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's…
There exists stable growing solution of primary resonant equation for a autoresonant pumping with decreasing amplitude. The primary term of asymptotics is $O(\sqrt{t})$ and does not depend on order of the force from some interval. We point…
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
In this work, we investigate resonance and antiresonance behaviour in forced coupled Duffing oscillators with nonlinear damping. Further, we will analyse the parameter dependence of the frequency response and stability. In the course of all…
We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to…
Some limit theorems are proven for the linear oscillator with random coefficients. The asymptotic behaviour of the moments is studied in detail. The technique presented in this paper can be applied to general linear systems with noise and…
In this paper the dynamic behavior of an oscillating tip-microlever system at the proximity of a surface is discussed. We show that the nonlinear behavior of the oscillator is able to explain the high sensitivity of the oscillating tip…
We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise…