Stochastic Resonance and time advance coding in chemical reactions

Stochastic Resonance (SR) is a phenomenon which may be found in nonlinear systems close to an excitation threshold. SR is a means for enhancing a weak periodic subthreshold signal from its noisy background by adding stochastic fluctuations, i.e. in biological and physical systems. It has been proposed that SR is important for the ability of neural systems to detect weak periodic signals. In the present work we show experimentally that SR occurs in two nonlinear chemical reactions, namely in the enzymatic Peroxidase-Oxidase (PO) reaction and in the Belousov-Zhabotinskii (BZ) reaction. A small sinusoidal signal with increasing noise is imposed on the focal steady state near a subcritical Hopf bifurcation. When the threshold is crossed beyond a certain noise amplitude, the system responds with spikes. The resulting interspike histogram and the plot of the signal to noise ratio, which is evaluated from the respective Fourier spectra, pass through a maximum at an optimal external noise level. An alternative way to cross the excitation threshold without noise is the variation of the bias value of the sinusoidal signal. The variation of the bias value causes the spikes to appear earlier if the sinusoidal function is moved closer towards the threshold. This so-called time advance coding is shown experimentally for the first time in the BZ reaction by imposing sinusoidal flow rate variations using different bias values. The phenomenon has been proposed by Hopfield to be a means for analog pattern recognition.