Fig 2. Simulations for different interactions of the neural oscillator with an external stimulus.

(a) Schematic representation of the model used to run the simulations shown in panels b and c: The neural oscillator is driven top-down and/or bottom-up by an external stimulus. The model assumes the same bottom-up interaction as in Fig 1, but this time, it can be modulated by a top-down mechanism. Mathematically, it implies that λ is shifted by the presence of an external input. (b) The oscillator receives a constant external input, and λ is top-down modified by the onset of the stimulus. Simulation parameters are ω_nat = 2π 4, γ = 1, k = 50, and s(t) a step function switching from 0 to 1. (c) The oscillator is only bottom-up driven by a rhythmic stimulation. Simulation parameters are ω_nat = 2π 4, γ = 1, k = 25, and s(t) a sinusoid is a sinusoid with a frequency fixed at 3.5 Hz. (d) Schematic representation of the model used to run the simulations shown in panel e: The neural oscillator is driven bottom-up by a single event. (e) Oscillator’s response when forced by a single stimulus. Once the external perturbation ceases, the oscillator resumes its natural ongoing activity but with a phase lag. The same stimulus resets the ongoing oscillation to different values (θ₀₁, θ₀₂) depending on the initial phase. Dashed lines: unperturbed oscillator’s activity. Simulation parameters are ω_nat = 2π 4, γ = 0.1, and k = 50. Blue traces: oscillator’s response, i.e., x(t). Magenta traces: external stimulus, i.e., s(t). Blue dots: time evolution of the oscillator’s period.