The application of the first order system transfer function for fitting the 3-arm radial maze learning curve

Abstract

A mathematical model is described based on the first order system transfer function in the form Y = B 3 ∗ exp ( − B 2 ∗ ( X − 1 ) ) + B 4 ∗ ( 1 − exp ( − B 2 ∗ ( X − 1 ) ) ) , where X is the learning session number; Y is the quantity of errors, B 2 is the learning rate, B3 is resistance to learning and B 4 is ability to learn. The model is tested in a light–dark discrimination learning task in a 3-arm radial maze using Wistar and albino rats. The model provided good fits of experimental data under acquisition and reacquisition, and was able to detect strain differences among Wistar and albino rats. The model was compared to Rescorla–Wagner, and was found to be mutually complementary. Comparisons with Tulving’s logarithmic function and Valentine’s hyperbola and the arc cotangent functions are also provided. Our model is valid for fitting averaged group data, if averaging is applied to a subgroup of subjects possessing individual learning curves of an exponential shape.