Quasiperiodic Forcing of a Chemical Reaction: Experiments and Calculations

Abstract

We present experimental and theoretical investigations of the nonlinear resonance behavior of a focal steady state in the Belousov-Zhabotinsky (BZ) reaction which is perturbed by its own dynamics. For this purpose the outputs of two independent BZ-oscillators of incommensurate frequencies are linearly combined in analogy to a simple feed-forward net to achieve the quasiperiodic driving of a third BZ-reactor which is in a focal steady state. For low amplitudes of the quasiperiodic flow-rate perturbations the response is also quasiperiodic in the focal BZ-reactor. Above a threshold value of the quasiperiodic amplitudes, however, single bursts are observed at small phase differences between the two perturbing oscillators. A further increase in the amplitude leads to groups of bursts with small oscillations in between. Aperiodic stochastic bursting in the BZ-reactor is observed when the flow-rate into the focal reactor is perturbed by Gaussian distributed white noise of sufficiently high amplitude and pulse length. The experiments are shown to agree with computer simulations using the Showalter-Noyes-Bar-Eli (SNB) model. At high amplitudes of quasiperiodic forcing the SNBmodel gives evidence for the existence of an attractor which is strange but nonchaotic (information dimension = 2.0).

Stochastic Resonance in Chemistry. 1. The Belousov−Zhabotinsky Reaction

“…We have demonstrated the phenomenon of stochastic resonance with a nonlinear chemical reaction in an excitable focal steady state close to a supercritical Hopf bifurcation. 17,21,22 Our experiments with the BZ reaction are in qualitative agreement with the SNB model. 32 The calculations as well as the experiments show that optimal noise levels for the enhancement of periodic signals also exist in nonlinear chemical reactions when certain conditions are fulfilled.…”

“…Experimental Results with the BZ Reaction. The BZ reaction was run in a focal steady state at a constant flow rate of k f ° = 2.48 × 10 -3 s -1 (τ = 6.7 min) which is 23% above the supercritical Hopf bifurcation. ,, After at least three residence times have elapsed, a sinusoidal flow rate modulation with ω = 8.38 × 10 -3 rad/s ( T = 750 s) was imposed on the focus. At a signal amplitude of α = 0.62 simple response oscillations of the same period were observed without external noise.…”

“…In recent work periodic and random perturbations of focal steady states have been investigated in the BZ, the peroxidase−oxidase (PO), and the methylene blue−sulfide−oxygen systems via the flow rate and the electrical current. − In the present study we investigate SR in the Belousov−Zhabotinsky (BZ) reaction in a focus where a sinusoidal signal together with noise is imposed on the flow rate of reactants into the reactor. The (excitable) focus is located close to a primary Hopf bifurcation beyond which small-amplitude period-1 oscillations are observed.…”

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“…Zhou et al [1992] studied experimentally an SNA in a quasiperiodically forced electronic circuit with a multistable potential, modeling a SQUID device. Zeyer et al [1995] forced quasiperiodically a Belousov-Zhabotinsky reaction, using a superposition of signals from two other chemical reaction cells operating periodically as a force. A simple electronic circuit with a two-frequency forcing has been studied by Yang and Bilimgut [1997].…”