The close agreement between the above model and the experimental data suggests that Weber's law behavior and light adaptation are the result of a feedback mechanism that is proportional to the background light level. However, we are now faced with the question of how to construct a model that incorporates the desired behavior at each light level but does not require feedback that depends explicitly on I0. To answer
Figure 22.5 A family of linear models, which describes the linear responses of turtle horizontal cells around a mean light level. (Adapted from Tranchina and Peskin, 1988.)
C Constant input
Figure 22.6 A nonlinear model that embeds the family of linear models shown in the previous figure. (Adapted from Tranchina and Peskin, 1988.)
this question, Tranchina and Peskin (1988) constructed a nonlinear model that has the same linear behavior as the above model but does not depend explicitly on I0. Their model, shown in Fig. 22.6, is similar to that in Fig. 22.5, but the feedback amplification is through a static nonlinearity rather than by the factor I0.
Suppose that the input to this system is I(t) = I0 + eelmt, and the output V is given by
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