Extended Stevens' power law.

Area of Science:

• Psychophysics
• Sensory Science
• Fractal Dynamics

Background:

• Stevens' power law is a cornerstone in psychophysics, relating physical stimulus intensity to perceived magnitude.
• Traditional power law models do not fully capture the sigmoid nature of many psychophysical functions.
• Existing models often fail to accurately represent stimulus-response relationships across wide ranges.

Purpose of the Study:

• To propose an extended Stevens' power law that incorporates sigmoid characteristics.
• To model stimulus-response relationships using a power-transformed Gompertz function.
• To validate the extended model for saltiness and brightness perception.

Main Methods:

• Employed an S-shaped Gompertz function mapped to a power form.
• Developed an extended Stevens' power law: y(C) = k(C)C^(n(C)).
• Utilized experimental psychophysical data for saltiness and brightness.

Main Results:

• The extended model accurately reproduces psychophysical data across a broad range of stimulus magnitudes.
• The scaling factor k(C) and exponent n(C) are demonstrated to be functions of stimulus magnitude C.
• The extended power law exhibits self-similar and allometric properties, indicative of fractal processes.

Conclusions:

• The proposed extended Stevens' power law offers a more accurate representation of psychophysical functions.
• The model successfully captures the non-linear stimulus-response dynamics in sensory perception.
• The fractal nature of the extended law provides new insights into sensory processing mechanisms.