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A nonlinear integral equation for visual impedance

✍ Scribed by Simeon M. Berman; Alan L. Stewart

Publisher
Springer-Verlag
Year
1979
Tongue
English
Weight
389 KB
Volume
33
Category
Article
ISSN
0340-1200

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✦ Synopsis

The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation.

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