Anatol M. Zhabotinsky (2007), Scholarpedia 2(9):1435 (revision #91050, last modified 21 October 2011) — DOI-10.4249/scholarpedia.1435
Key takeaways
- The BZ reaction made homogeneous chemical oscillation respectable. Before it, chemists read the detailed-balance argument, which forbids oscillation near equilibrium, as forbidding oscillation in any closed homogeneous system, and blamed observed oscillations on heterogeneity or error.
- The oscillation is a relaxation cycle. Autocatalytic production of HBrO₂ oxidizes the catalyst (Ce³⁺ → Ce⁴⁺). Br⁻ inhibits that autocatalysis, and Br⁻ is produced when Ce⁴⁺ is reduced by malonic and bromomalonic acid. Phase-resetting by injected Br⁻, Ag⁺ and Ce⁴⁺ confirms the scheme.
- Closed, it oscillates for up to thousands of cycles and then stops; open (CSTR), it oscillates indefinitely and shows bursting and chaos. Unstirred, it propagates trigger waves that form target patterns and, when broken, spirals and scroll waves.
Standing in the record
Filed on 2026-10-02 at the owner’s request, as the Belousov–Zhabotinsky entry among the canonical systems of the dissipative-structure programme. The request offered Zhabotinsky (1964) or Zaikin & Zhabotinsky (1970). Neither was readable, so this review by Zhabotinsky, which covers both, stands in.
It bears on the record’s coverage in three ways.
- What makes BZ a dissipative structure, and when. The review’s split between closed and open systems is the useful point. A closed BZ mixture oscillates on its way to equilibrium: a long transient, not a steady state. Only the continuous-flow reactor holds it permanently away from equilibrium, which is Prigogine’s condition (LIT-516). Cross and Hohenberg (LIT-527, §X.B.5) make the same point for patterns: closed experiments “run down in finite time”, and open gel reactors were the fix.
- The demarcation question in LIT-192. BZ is the cleanest case of a chemical system with behaviour organisms are often singled out for: rhythm, excitability, self-propagating signals, entrainment of slower pacemakers by faster ones. It does this with no closure of constraints and nothing that maintains itself; fed reagents, it simply runs. That supports the view NOTE-094 records, that dissipative self-organization cannot be the demarcating property, and it makes BZ the natural foil for any account that tries to make it one.
- LIT-211’s “Dissipative Self-Organizing Systems” cluster. BZ satisfies thermodynamic-organizational definitions of life of that kind about as well as a candle flame does. It is the standard counter-example such definitions must exclude.
The review’s first paragraph credits Nicolis and Prigogine (LIT-524) with the far-from-equilibrium condition on oscillation.
No instruction for machine-learning practice. The anthology does not hold it.