Stochastic resonance in a sinusoidal potential system: An analog simulation experiment (original) (raw)
Related papers
The role of damping on Stochastic Resonance in a periodic potential
Physica A: Statistical Mechanics and its Applications, 2014
We have studied the dynamics of a particle in a periodically driven underdamped periodic potential. Recent studies have reported the occurrence of Stochastic Resonance (SR) in such systems in the high frequency regime, using input energy per period of external drive as a quantifier. The particle trajectories in these systems can be in two dynamical states characterised by their definite energy and phase relation with the external drive. SR is due to the noise assisted transition of the particles between these two states. We study the role of damping on the occurrence of SR. We show that a driven underdamped periodic system exhibits SR only if the damping is below a particular limit. To explain this we study the syatem in the deterministic regime. The existence of the two dynamical states in the deterministic regime is dependent on the amount of damping and the amplitude od external drive. We also study the input energy distributions and phase difference of the response amplitude with the external drive as afunction of the friction parameter.
Relative stability of dynamical states and stochastic resonance in a sinusoidal potential
Physical Review E, 2013
Recently, stochastic resonance was shown to occur in underdamped periodic potentials at frequencies (of the drive field) close to the natural frequency at the minima of the potentials. In these systems the particle trajectories are not arbitrary at low temperatures but follow the drive field with two definite mean phase differences depending on the initial conditions. The trajectories are thus found to be in only two stable dynamical states. The occurrence of stochastic resonance in the periodic potentials was explained as a consequence of the transitions between these two dynamical states as the temperature was increased. In the present work, we find the range of amplitudes of the drive field over which the dynamical states could be observed in a sinusoidal potential. The variation of the relative stability of the dynamical states as a function of drive-field amplitude is clarified by analyzing the nature of curves characterizing the stochastic resonance as the amplitude is varied within the range.
Stochastic resonance in periodic potentials
Physical Review E, 2011
The phenomenon of stochastic resonance (SR) is known to occur mostly in bistable systems. However, the question of the occurrence of SR in periodic potential systems has not been resolved conclusively. Our present numerical work shows that the periodic potential system indeed exhibits SR in the high-frequency regime, where the linear-response theory yields maximum frequency-dependent mobility as a function of noise strength. The existence of two (and only two) distinct dynamical states of trajectories in this moderately feebly damped periodically driven noisy periodic potential system plays an important role in the occurrence of SR.
High frequency stochastic resonance in periodically driven systems
Jetp Letters, 1993
High frequency stochastic resonance (SR) phenomena, associated with fluctuational transitions between coexisting periodic attractors, have been investigated experimentally in an electronic model of a single-well Duffing oscillator bistable in a nearly resonant field of frequency omegaF\omega_FomegaF. It is shown that, with increasing noise intensity, the signal/noise ratio (SNR) for a signal due to a weak trial force of frequency OmegasimomegaF\Omega \sim \omega_FOmegasimomegaF at first decreases, then {\it increases}, and finally decreases again at higher noise intensities: behaviour similar to that observed previously for conventional (low frequency) SR in systems with static bistable potentials. The stochastic enhancement of the SNR of an additional signal at the mirror-reflected frequency vertOmega−2omegaFvert\vert \Omega - 2 \omega_F \vertvertOmega−2omegaFvert is also observed, in accordance with theoretical predictions. Relationships with phenomena in nonlinear optics are discussed.
The mechanism of stochastic resonance
Journal of Physics A: Mathematical and General, 1981
It is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance (peak in the power spectrum) which is absent when either the forcing or the perturbation is absent.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2012
We have studied the motion of an underdamped Brownian particle in (i) a bistable periodic potential and (ii) washboard potentials subjected to a sinusoidal external field. The particles are shown to be effectively in two dynamical states of their trajectories with distinct amplitudes and phase relationship with the external drive. These dynamical states are stable with fixed energies at low temperatures, but transitions between them take place as the temperature is increased. The average input energy loss to the environment per period of the drive shows a stochastic resonance (SR) peak as a function of temperature for the underdamped system potentials studied. The occurrence of SR in these systems is explained using the statistics of transitions between the two dynamical states.
Nonconventional stochastic resonance
Journal of Statistical Physics, 1993
It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found, and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; and (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated.
Stochastic resonance in electrical circuits. I. Conventional stochastic resonance
Circuits and Systems …, 1999
Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory.
Stochastic resonance without external periodic force
Physical Review Letters, 1993
A model of a two-dimensional autonomous system subject to external noise is investigated. Without noise the system has a stable limit cycle in a certain region of control parameter. Various noise-induced eAects have been found numerically, such as a noise-induced frequency shift in the presence of the deterministic limit cycle, and noise-induced coherent oscillations in the absence of the deterministic limit cycle. An interesting result is that the stochastic resonance phenomenon appears in a system without an external signal and when the asymptotic state of the deterministic system is stationary.