Source
Zhabotinsky (2007), “Belousov-Zhabotinsky reaction”, LIT-531 (Scholarpedia 2(9): 1435, revision of 21 October 2011), read in full in NOTE-414. The page has later contributors, so not every sentence is certainly Zhabotinsky’s. The figures were read through their captions. The primary papers it cites were not read.
What was actually shown
The core loop. Zhabotinsky (1964) replaced Belousov’s citric acid with malonic acid and showed that the colour oscillation is the oscillation of [Ce⁴⁺], that oxidation of Ce³⁺ by bromate is autocatalytic, that oscillation starts once bromomalonic acid has accumulated, and that Br⁻ inhibits the autocatalysis. The core scheme (Vavilin and Zaikin 1971) has HBrO₂ autocatalytically oxidizing the catalyst, HBrO₂ removed by Br⁻, and Br⁻ produced as the oxidized catalyst oxidizes bromomalonic acid.
The test (Fig. 1). Phase resetting: Br⁻ or Ce⁴⁺ injected while [Ce⁴⁺] rises switches the system to the falling phase, and Ag⁺, which removes Br⁻, switches it from falling to rising. That is what a fast positive feedback switched off by a slower negative one predicts. NOTE-414 rates the mechanism strong.
Closed against open. In a closed, stirred batch, oscillation occurs over wide ranges of initial concentrations and “can generate up to several thousand oscillatory cycles”, then stops. In a continuous-flow stirred tank reactor, “stationary oscillations can continue indefinitely”, and bursting and chaos appear.
Unstirred media. Thin layers carry trigger waves from point pacemakers, forming target patterns (Zaikin and Zhabotinsky 1970). Colliding waves annihilate, the fastest pacemaker entrains the rest, and broken fronts curl into spirals, and in thick layers into scroll waves.
The model. The Oregonator “properly models oscillations and excitability” but “is not a quantitative model”: it leaves total catalyst out, reproduces the waveform poorly and misses the oscillatory domains. Taking the reversibility of the catalyst reactions into account corrects these.
What could have come out otherwise. Injected bromide could have failed to reset the phase, or reset it the wrong way. It did not.
What this does not say
- That a closed batch is a dissipative structure in Prigogine’s steady-state sense. It runs down. How long it stays near a quasi-steady state is an open question in NOTE-414.
- A thermodynamic account. The far-from-equilibrium condition is cited to Nicolis and Prigogine (LIT-524), unread. The review gives no entropy production, free-energy budget or stability analysis.
- That the Oregonator is quantitatively right. It is not, by the review’s own account.
- That BZ is alive, or organized like an organism. It has rhythm, excitability, self-propagating signals and entrainment, but its organization is kept up by the experimenter’s feed.
- A precise cycle count. “Several thousand” is uncited. Cross and Hohenberg (LIT-527) give under 100 periods for unstirred pattern experiments; the setups differ, and the figures do not conflict.
Connections
- THEORY-072 holds that organisms differ from dissipative structures such as a candle flame by organisational differentiation, and names a BZ medium as one such structure. This account is why the comparison is with a fed reactor and not a batch. BZ in a flow reactor is the cleanest chemical case that thermodynamic and dynamical criteria alone do not separate from organisms (NOTE-414).
- THEORY-088 compares spiral defects in slow cortical activity with BZ spirals and cites this review.
- Prigogine’s lecture (LIT-516) has the Brusselator, with its inputs “held constant”. BZ in a flow reactor is its experimental counterpart. Turing (LIT-535) did not cover excitable, strongly non-linear waves of this kind, and BZ in microemulsion has since given stationary Turing structures.