相关论文: The autoresonance threshold into a system of weakl…
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…
We investigate an influence of dissipation on autoresonant threshold for a system of nonlinear oscillators. Exact asymptotic formulas and numerical simulations are presented. These results correspond to an initial interval of autoresonance.
Autoresonance is a phase locking phenomenon occurring in nonlinear oscislatory system, which is forced by oscillating perturbation. Many physical applicatcons of the autoresonance are known in nonlenear physics. The essence of the…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The…
We study an autoresonant asymptotic behaviour for nonlinear oscillators under slowly changing frequency and amplitude of external driver. As a result we obtain formulas for threshold values of amplitude and frequency of the driver when…
Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the…
We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…
A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with 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…
The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…
We propose a scheme for obtaining highly-sensitive oscillators in a coupled-resonator system with an exceptional point of degeneracy (EPD) and a small instability. The oscillator with the exceptional degeneracy is realized by using two…
The mechanism by which a resonance may be attracted to a sharp threshold is described with several examples. It involves a threshold cusp interfering constructively with either or both (i) a resonance produced via confinement, (ii)…
In this paper we investigate the distribution of energy between weakly coupled linear and nonlinear oscillators in a two-degree-of-freedom (2D) system. Two classes of problems are studied analytically and numerically: (1) a periodic force…
The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\varepsilon$. It is well known that,…
An anharmonic oscillator when driven with a fast, frequency chirped voltage pulse can oscillate with either small or large amplitude depending on whether the drive voltage is below or above a critical value-a well studied classical…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for…
We consider a model for two lasers that are mutually coupled optoelectronically by modulating the pump of one laser with the intensity deviations of the other. Signal propagation time in the optoelectronic loop causes a significant delay…
The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviours…