1,720,968 research outputs found
Drastic facilitation of the onset of global chaos
No full textWe show that the onset of global chaos in a time periodically perturbed Hamiltonian system may occur at unusually small magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. We develop the asymptotic theory and verify it in simulations
Short time scales in the Kramers problem: A stepwise growth of the escape flux
No full textWe prove rigorously and demonstrate in simulations that. for a potential system staying initially at the bottom of a well, the escape flux over the barrier grows on times of the order of a period of eigenoscillation in a stepwise manner, provided that friction is: small or moderate. If the initial state is not at the bottom of the well, then, typically, some of the steps transform into oscillations. The stepwise/oscillatory evolution at short times appears to be a generic feature of a noise-induced flux
Strong enhancement of noise-induced escape by nonadiabatic periodic driving due to transient chaos
No full textWe have found a mechanism by which a moderately weak nonadiabatic periodic driving may significantly facilitate noise-induced interwell transitions in an underdamped multiwell system. The mechanism is associated with the onset of a homoclinic tangle in the noise-free system: if the ratio of the driving amplitude A to the damping Gamma exceeds a critical value similar to 1, then the basins of attraction of the linear responses related to different wells are mixed in a complex manner in some layer associated with the separatrix of the undriven nondissipative system, and the minimal energy in such layer is lower than the top of the barrier. Thus the energy to which the system needs to be activated by the noise, to be able to make a transition, is lower than the top of the barrier
Zero-dispersion nonlinear resonance
No full textUnderdamped oscillators that possess a maximum or minimum in their dependence of eigenfrequency on energy have recently been shown to exhibit a range of unusual phenomena. Because they are associated with the presence of an extremum in whose vicinity the eigenfrequency is almost energy-independent, they have been named zero-dispersion phenomena. They manifest themselves both in the deterministic dynamics and in the presence of noise. When the oscillator is driven by a weak periodic force at a frequency close to that of the extremum, a novel type of nonlinear resonance, zero-dispersion nonlinear resonance (ZDNR) can occur. A giant response then arises even in the absence of resonance between the drive frequency and any eigenoscillation of the system. The properties of ZDNR, the nature of the transition from ZDNR to conventional nonlinear resonance as relevant parameters are varied, the occurrence of dynamical chaos associated with ZDNR, and the influence of noise, are analysed and discussed for both Hamiltonian and dissipative systems
Short time scales in the Kramers problem: A stepwise growth of the escape flux (vol 86, pg 1665, 2001)
No full textCharacteristic types of evolution of noise-induced escape flux at short time scales
No full textUnlike the quasi-stationary escape flux, the flux on time scales preceding the quasi-stationary stage may significantly depend on the initial state of the system. We analyze three characteristic initial states: (i) the stable state of the noise-free system, i.e. the bottom of the potential well; (ii) the non-bottom state with given coordinate and velocity; (iii) a thermalized state. We prove rigorously and demonstrate in simulations that, on the time scale of a period of eigenoscillation, the flux grows stepwise for cases (i) and (iii), and in an oscillatory manner for case (ii). Different steps/oscillations correspond to different topologies of the most probable escape path
ZERO-FREQUENCY SPECTRAL PEAKS OF UNDERDAMPED NONLINEAR OSCILLATORS WITH ASYMMETRIC POTENTIALS
No full textThe spectral density of the fluctuations of an underdamped, single-well, nonlinear oscillator driven by a random force has been investigated. Electronic analog experiments have demonstrated the existence of a narrow spectral peak at zero frequency; such a peak only appears, however, in those cases where the potential is non-centro-symmetric. The evolution of the peak with variation of a parameter characterizing the asymmetry of the potential, and with noise intensity, has been investigated both experimentally and theoretically. It is found that the half-width of the peak remains relatively small (of the order of the reciprocal relaxation time) over a broad range of noise intensities. The theory of the peak shape is shown to be in close agreement with experiment. The relationships of the peak to the (apparently similar) zero-frequency peaks observed previously in double-well oscillators, where they are responsible for stochastic resonance, and to the supernarrow spectral peaks found near kinetic phase transitions in periodically driven systems, are discussed
Zero-dispersion phenomena in oscillatory systems.
Full text linkPhenomena occurring in a particular class of nonlinear oscillatory systems—zero-dispersion systems—are reviewed for cases with and without damping while the system is driven either by random fluctuations (noise), or by a periodic force, or by both together. Zero-dispersion (ZD) systems are those whose frequency of oscillation ω possesses an extremum as a function of energy E. Oscillations at energies close to the extremal energy Em, where the “frequency dispersion” dω/dE is equal to zero, correlate with each other for very long times, to some extent like in a harmonic oscillator. But unlike the latter, the correlation time decreases as the energy shifts away from Em. It is the combination of this local harmonicity, with the fact that a perturbation can cause transitions between strongly and weakly correlated behaviour, that gives rise to the rich manifold of interesting ZD phenomena that are reviewed. A diverse range of physical systems may be expected to exhibit ZD behaviour under particular circumstances. Examples considered in detail include superconducting quantum interference devices, the 2D electron gas in a magnetic superlattice, axial molecules, electrical circuits, particle accelerators, impurities in lattices, relativistic oscillators, and the Harper oscillator. The ZD effects to be anticipated in quantum systems are also discussed. Each section ends with a suggested outlook for future research
Divergence of the Chaotic Layer Width and Strong Acceleration of the Spatial Chaotic Transport in Periodic Systems Driven by an Adiabatic ac Force
No full textSUMMARY We show for the first time that a {\it weak} perturbation in a Hamiltonian
system may lead to an arbitrarily {\it wide} chaotic layer and {\it fast}
chaotic transport. This {\it generic} effect occurs in any spatially periodic
Hamiltonian system subject to a sufficiently slow ac force. We explain it and
develop an explicit theory for the layer width, verified in simulations.
Chaotic spatial transport as well as applications to the diffusion of particles
on surfaces, threshold devices and others are discussed
Bifurcation analysis of zero dispersion-nonlinear resonance.
No full textThe problem of zero-dispersion nonlinear resonance - a phenomenon that can occur in a periodically-driven nonlinear oscillator whose eigenfrequency as a function of energy possesses an extremum - has been formulated in general for both the dissipative and nondissipative situations. A complete bifurcation analysis and classification of period-l orbits is presented. The significance of bifurcations for the onset of chaos in the system, and for fluctuations in the presence of external noise, is discussed
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