Three Classical Nonreciprocally Coupled Oscillators

Mean-field equations of three nonreciprocally coupled oscillators, see Fig. 9.13.

Open chain of three oscillators described by Eq. (9.8.3). (a) Phase diagram where each color denotes a different phase. White pixels were not assigned any phase. Panels (b) to (g) show the time evolutions of one phase each corresponding to the symbol next to the panel label. The values of g_– and g̃ equal the coordinates of the respective symbol in (a). (b) Phase locking to Δϕ_j = ϕ_j - ϕ_j+1 = π. (c) Wobble motion: varying amplitudes and oscillating phases around Δϕ_j ≈ π. (d) Both wobble motion (c) and traveling-wave states (f) exist. (e) Modulated traveling-wave states: varying amplitudes and oscillating phases around Δϕ_j ≈ ±2π/3. (f) Traveling-wave states: constantly increasing phases with fixed Δϕ_j ≈ ±2π/3. (g) Phase locking to Δϕ_j = 0. A list of rules and thresholds for each class of steady states is given in Sec. 9.8.3.