Experimental study of a nonlinear system in the presence of noise: The stochastic resonance

Abstract

Noise in a dynamical system is usually regarded as a nuisance. However, in certain nonlinear systems the addition of noise in the system can give counterintuitive dynamics. An illustrative phenomenon is stochastic resonance (SR). In this paper we present, an experiment demonstrating stochastic resonance in a bistable electronic device: the tunnel diode. This experiment is suitable both as a lecture demonstration and for student investigations. We introduce the statistical properties of the noise and the physical picture of the SR phenomenon. We describe the experimental setup and present typical results.

Linear and nonlinear experimental regimes of stochastic resonance

“…In this equation R is the biasing resistor, C is the parallel capacitor (in our case 45 pF) of the circuit and v n (t) is a noise voltage mimicking the presence of a finite temperature in the corresponding overdamped system with a physical particle. The generalized potential U (v d , t) associated to our physical system is [16] …”

Interplay between detection strategies and stochastic resonance properties

“…where τ K is the Kramers prefactor [37], that also gives the order of magnitude of the relaxation time of local equilibrium [38].…”

A review of stochastic resonance: circuits and measurement

“…Examples of bistable systems occur in areas such as physics [bistable super-conducting quantum interface device (SQUID) loops [29], bidirectional ring lasers [17]], biology (sensory systems [28], [30]), Earth sciences [climate [14], [29], [36]] and electronics (Schmitt trigger [16], tunnel diode [37], [38]). Here, a simple double well potential in a nonlinear system is described [16], [18], [23], [39].…”

“…A model of a one-dimensional nonlinear system that exhibits stochastic resonance is the damped harmonic oscillator with the Langevin equation of motion (1) where the dot represents the time derivative [37]. This equation describes the motion of a particle of mass moving in the presence of friction .…”

“…All that is needed is a system with a cubic characteristic that has three operating points for some parameter. A tunnel diode with a load line defining the operating points would be an example of an electrical system that fits this requirement [37].…”