Explore Belousov-Zhabotinsky chemical oscillation, spiral waves, and reaction-diffusion patterns
Discovered by Boris Belousov (1951) and later studied by Anatoly Zhabotinsky, the BZ reaction is a classic example of non-equilibrium thermodynamics. Visible color oscillations arise from redox cycling of the catalyst-indicator mixture. This page uses a reduced activator-inhibitor reaction-diffusion description rather than the full multi-species chemistry.
This page uses a reduced two-variable activator-inhibitor form related to Oregonator-type kinetics: dX/dt = (X(1-X) - (X-q)fZ/(X+q)) / epsilon + Dx·nabla²X; dZ/dt = X - Z + Dz·nabla²Z. Here X is the activator-like variable, Z is the recovery/inhibitor-like variable, f is the stoichiometric factor, q is the scaling parameter, and epsilon controls timescale separation. This reduced model produces excitable media capable of spiral waves.
Spiral waves appear in many excitable media: cardiac tissue (arrhythmias), neural cortex (epileptic seizures), calcium waves in cells, and catalytic surface reactions. Understanding BZ spiral wave dynamics helps model and potentially control these biological phenomena. Spiral breakup into chemical chaos parallels ventricular fibrillation.
Alan Turing (1952) showed that diffusion-driven instability can generate stationary patterns (spots, stripes). The BZ reaction in a reverse microemulsion (AOT system) produces Turing patterns where the inhibitor diffuses faster than the activator. This demonstrates the rich pattern-forming capability of reaction-diffusion systems.
The reaction field shows chemical waves propagating as colored fronts. Red = high X (activator), blue = low X. Watch for spiral wave formation from broken wavefronts. The concentration plot shows oscillatory X and Z at a probe point. The phase portrait shows the limit cycle trajectory.
1) Start with Spiral preset and observe rotating spiral waves. 2) Increase f to see wave period changes. 3) Reduce epsilon for sharper fronts. 4) Use Chaos preset for spiral breakup. 5) Set Excitable to see single propagating pulses that die out. 6) Click on the reaction field to add local perturbations.