The Rössler system (1976) is a minimal 3D model of chemical chaos: ẋ=−y−z, ẏ=x+ay, ż=b+z(x−c). As c increases: limit cycle → period-2 → period-4 → ... → chaos via period-doubling cascade. Lyapunov exponent λ₁ transitions from negative to positive at the onset of chaos.
Bifurcation (vary c)
c = 4.00
λ₁ ≈ computing…
Regime: limit cycle
Period-doubling route to chaos. c≈4: period-1, c≈6: period-2, c≈8.5: period-4, c≈9: chaos. Universal Feigenbaum ratio δ≈4.669.