Figure 1.

Adaptation of two standard adaptive frequency oscillators. The upper panels show the time course of the frequency determining parameter θ. The time during which the external signal is applied to the system is indicated by the yellow shaded area. The dashed horizontal lines indicate the values θ₀ and θ_ext corresponding to the initial intrinsic frequency f₀ and the target frequency f_ext of the external signal, respectively. The panels below show the oscillating state variables x and y and the external signal F at different short time windows during the adaptation process. In both cases, the initial intrinsic frequency of the oscillator is f₀ = 4.0 and the external signal is a sine wave with unit amplitude and frequency f_ext = 2.0. (A) Adaptive frequency Hopf oscillator with μ = 1.0 and ϵ = η = 1.0 (see Methods). The initial value of the parameter θ is given by θ₀ = 2πf₀ ≈ 25.1. Accordingly, the value corresponding to the frequency of the external signal is θ_ext = 2πf_ext ≈ 12.6. The external signal is applied for 100 ≤ t < 700. (B) Adaptive frequency Van der Pol oscillator with μ = 100.0 and ϵ = η = 0.7 (see Methods). The values of the parameter θ corresponding to f₀ and f_ext are θ₀ ≈ 34.8 and θ_ext ≈ 22.0 (see Methods). The external signal is applied for 100 ≤ t < 500.