Related papers: The Van der Pol Equation
The principle of constructing a new class of systems with hyperbolic chaotic attractors is proposed. It is based on using oscillators, the transfer of excitation between which is provided resonantly due to the difference in the frequencies…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
We study analytically the coexistence of multiple periodic solutions and invariant tori in the general Van der Pol-Duffing oscillator equations. We use several results related to the averaging method in order to analytically obtain our…
Asymptotic random dynamics of weak solutions for a damped stochastic wave equation with the nonlinearity of arbitrarily large exponent and the additive noise on $\mathbb{R}^n$ is investigated. The existence of a pullback random attractor is…
The aim of this section is to present programs allowing to high- light the slow-fast evolution of the solutions of nonlinear and chaotic dynamical systems such as: Van der Pol, Chua and Lorenz models. These programs provide animated phase…
We present a perturbation analysis of the semiclassical Wigner equation which is based on the interplay between configuration and phase spaces via Wigner transform. We employ the so-called harmonic approximation of the Schrodinger…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From bifurcation…
The complication of chaotic oscillation under its transformation by linear inertial process is discussed. It is shown that such complication is begun from large scales of attractor and is pure dynamical process.
Recently, a system with uniformly hyperbolic attractor of Smale-Williams type has been suggested [Kuznetsov, Phys. Rev. Lett., 95, 144101, 2005]. This system consists of two coupled non-autonomous van der Pol oscillators and admits simple…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…
This paper aims to study time periodic solutions for 3D inviscid quasi-geostrophic model. We show the existence of non trivial rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the…
We study the effect of noise for a physically realizable flow system with a hyperbolic chaotic attractor of the Smale - Williams type in the Poincare cross-section [S.P. Kuznetsov, Phys. Rev. Lett. 95, 2005, 144101]. It is shown numerically…
We study an opto-electronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly-stable fixed point, which, when subjected to a finite-amplitude…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small…
The ability to produce nonclassical wave in a system is essential for advances in quantum communication and computation. Here, we propose a scheme to generate highly nonclassical phonon emission statistics -- antibunched wave in a quantum…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
The longitudinal oscillations of air columns composed of contractions and rarefaction make up sound. Sound amplification is widely used in medical, electronic and communication fields. A simplistic technique for producing and amplifying can…