The Stochastic Resonance Phenomenon of Different Noises in Underdamped Bistable System

In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. We also found that the type of the noise has little effect on the resonance peak of the output power spectrum density, which is not observed in conventional harmonic systems driven by multiplicative noise with only an overdamped term. Therefore, the conclusion of this paper can provide experimental basis for the further study of stochastic resonance.

On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this ‘deterministic’ approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Regulation of Chemical Autapse on an FHN-ML Neuronal System

To explore the feasibility of physiological manipulation of autaptic structures, the effects of autaptic connections on an FHN-ML neuronal system with phase noise stimulation are studied systematically. Firstly, according to the dynamic analysis of the FHN-ML neuron model, a saddle-node bifurcation can occur on an invariant circle. Under the action of external oscillatory current with phase noise, the neuronal firing activity is sensitive to phase noise with less intensity, and an appropriate noise intensity can induce a significant stochastic resonance phenomenon. Secondly, the chemical autaptic function can effectively regulate the neuronal discharge activity. An inhibitory autapse can not only induce the transition from depolarized resting to periodic spiking, but can also induce the FHN-ML neuron suppressed by strong phase noise to generate a pronounced intermittent high-level burst-like discharge mode when the autaptic conductance is greater than 0.1. Finally, for a two-dimensional regular FHN-ML neuronal network, a small amount of autaptic structures can induce some special waveforms to restore the propagation of nerve impulses interrupted by phase noise disturbance. This indicates the significant regulation of autapses on spatial patterns of the FHN-ML neuronal network. The study can provide some theoretical guidance for building autaptic structures in local areas to modulate the dynamic behaviors of biological neuronal systems.

Investigation of a Nonlinear Vibrational Energy Harvester in the Stochastic Resonance Regime

In this paper the possibility to exploit advantageously the Stochastic Resonance phenomenon in a Nonlinear Energy Harvester to scavenge energy from wide band mechanical vibrations is experimentally demonstrated. The device is demonstrated to be capable of scavenging energy in case of a subthreshold sinusoidal vibration and a wideband noise (limited at 100 Hz) superimposed. The existence of an optimal value of the noise intensity maximizing the switching ratio of the bistable beam, then the performances, is experimentally demonstrated. The harvester is observed to generate power up to about 60 µW and 150 µW in case of a subthreshold sinusoidal input at 1 Hz and 3 Hz with a superimposed noise limited at 100 Hz.

On the stochastic resonance phenomenon in parametrically excited systems

The stochastic resonance phenomenon implies “positive” changing of a system behaviour when noise is added to the system. The phenomenon has found numerous applications in physics, neuroscience, biology, medicine, mechanics and other fields. The present paper concerns this phenomenon for parametrically excited stochastic systems, i.e. systems that feature deterministic input signals that affect their parameters, e.g. stiffness, damping or mass properties. Parametrically excited systems are now widely used for signal sensing, filtering and amplification, particularly in micro- and nanoscale applications. And noise and uncertainty can be essential for systems at this scale. Thus, these systems potentially can exhibit stochastic resonance. In the present paper, we use a “deterministic” approach to describe the stochastic resonance phenomenon that implies replacing noise by deterministic high-frequency excitations. By means of the approach, we show that stochastic resonance can occur for parametrically excited systems and determine the corresponding resonance conditions.