The effect of additive noise on dynamical hysteresis
نویسندگان
چکیده
We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value. Date. July 27, 2001. 2000 MSC. 37H20 (primary), 60H10, 34C55, 34E15, 82C31 (secondary).
منابع مشابه
Nonlinear Dynamic Modeling and Hysteresis Analysis of Aerospace Hydro - dynamical Control Valves
A new procedure for deriving nonlinear mathematical modeling for a specific class of aerospace hydro - mechanical control valves is presented. The effects of friction on the dynamic behavior of these types of valves along with the experimental verifictions are also given. The modeling approach is based on the combination of the following three tasks: decomposition of the valve into simple speci...
متن کاملCONTROL OF CHAOS IN A DRIVEN NON LINEAR DYNAMICAL SYSTEM
We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...
متن کاملDiscriminating additive from dynamical noise for chaotic time series.
We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only f...
متن کاملCapacity Bounds and High-SNR Capacity of the Additive Exponential Noise Channel With Additive Exponential Interference
Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is introduced as a new variant of such communication scenarios. First, it is shown that the additive Gaussian ch...
متن کاملThe effect of noise on strange nonchaotic attractors
The dynamical response of an underdamped Duffing oscillator to a quasiperiodic force is investigated in the presence and absence of very weak additive noise. Particular attention is focused on the effect of noise on the characteristics of strange nonchaotic attractors (SNAs). It is concluded that even extremely weak noise is sufficient to induce dynamical complexity in an SNA. PACS: 05.45.+b, 0...
متن کامل