Fig. 5: The largest Lyapunov exponent in one dimension.
From: Effervescence in a binary mixture with nonlinear non-reciprocal interactions
a Kymograph showing the evolution of the field ϕ1 in one dimensional space and time for α0 = 4 and α1 = 3. The propagating bands, and the production and dissolution of reciprocal granules (in red boxes highlighted with red arrows) droplets (in green boxes) are clearly visible. b Kymograph of dynamics in one spatial dimension for α0 = α1 = 4, showing numerous droplets appearing and dissolving. c The largest Lyapunov exponent Ω (for definition see Methods II) as a function of α1, while α0 is fixed at 2.5. Ω cross from a negative to a positive value corresponding to the α1 for which we see a transition from travelling waves to effervescence. d Ω calculated by varying α1 while α0 is fixed. Ω crosses from a negative to positive value when a transition occurs from travelling waves to effervescent waves and again changes sign when effervescence gives way to travelling ways.
