Two Classical Nonreciprocally Coupled Oscillators

Mean-field equations of two nonreciprocally coupled oscillators, see Fig. 9.12.

Two oscillators with external drive Ω_A = 0.5ɣ^A_g described by Eqs. (9.4.7) and (9.4.8). (a) Phase diagram where each color denotes a different phase. White pixels were not assigned any phase. The gray line denotes g̃ = g_AB. (b) Spectrum 𝒮_AA(ω_A) for g̃ = 0.7ɣ^A_d (location of upper symbols in (a)). The dashed white curves indicate ω_± and 2ω_± defined in Eq. (9.5.8). Panels (c) to (e) show the time evolutions of one phase each corresponding to the symbol next to the panel label. The values of g_AB and g̃ equal the coordinates of the respective symbol in (a). (c) Phase locking to ϕ_A = ϕ_B = -π/2. (d) Wobble motion: varying amplitudes and oscillating phases around ϕ_AB ≈ ±π/2. (e) Partial traveling-wave states: constantly increasing ϕ_A, oscillating ϕ_B around -π/2. The yellow phase (top left) corresponds to phase locking to ϕ_AB = π, similar to Fig. 9.11(c), where for g̃>g_AB (g̃<g_AB) ϕ_A = -π/2 (ϕ_A = π/2). The darker orange phase (center right) hosts modulated traveling-wave states, similar to Fig. 9.11(d). A list of rules and thresholds for each class of steady states is given in.