Sinusoidal

The Sinusoidal rule generates an oscillating signal based on a sine wave. It is used as an activity generator, not driven by input but producing rhythmic output over time. This is useful in simulations involving rhythmic inputs, periodic behavior, or neural oscillations.

At each time step, the neuron’s activation is updated by:

\[a(t) = \left(\frac{U - L}{2}\right) \cdot \sin(f \cdot t + \phi) + \left(\frac{U + L}{2}\right)\]

Where:

• \(a(t)\) is the neuron’s activation at time \(t\),
• \(U\) and \(L\) are the upper and lower bounds,
• \(f\) is the frequency of oscillation,
• \(\phi\) is the phase (initial position in the sine cycle),
• Optional noise can be added after computing the sine value.

This rule produces a smooth continuous waveform within a bounded range, centered between the upper and lower limits.

Parameters

• Phase: The initial offset in the sine wave cycle (in radians).
• Frequency: Controls how fast the activation oscillates over time.

For all other parameters, see common neuron properties

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