We demonstrate the phenomenon of stochastic resonance in a nonlinear chemical reaction. The term “stochastic resonance” (SR) denotes the detection of a weak periodic signal in a noisy system displaying a threshold. If the sum of the periodic signal and the noise amplitude crosses the threshold, an output pulse is triggered. At an optimal noise amplitude the distribution of pulse intervals as well as the signal-to-noise ratio will pass through a maximum. In the continuously stirred tank reactor (CSTR) experiments we superimpose a periodic flow rate signal on an excitable focal steady state located near a Hopf bifurcation in the Belousov−Zhabotinsky (BZ) reaction. In the Showalter−Noyes−Bar-Eli model of this reaction we vary the perturbation frequency and amplitude as well as the pulse length of the applied noise to elaborate the optimal conditions for stochastic resonance to occur in the model.

On the basis of previous theoretical work we present a simple method of chaos control in experiment and simulation using the Belousov−Zhabotinsky (BZ) reaction. The chaos control parameter employed is the sinusoidally modulated electric current (AC) acting on a Pt-working electrode. The experimental chaos control takes place in the well-known low flow rate region of the BZ reaction in a CSTR (continuous flow stirred tank reactor). It was possible to stabilize several unstable periodic orbits (UPO) in the BZ experiment, namely P1, P2, P3, and P4. The chosen model of chemical chaos is the seven-variables model (Montanator) of Györgyi and Field. The stabilized UPO (P3) in the model calculations is compared to the same UPO stabilized by time-delayed feedback method according to Pyragas. In addition we use the continuous time-delayed feedback method to achieve the tracking of the UPO starting in the chaotic range and continuing beyond.

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Stochastic Resonance (SR) is a phenomenon wich 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 Hopfield11 to be a means for analog pattern recognition.