SYSTEMS THEORY OF HOMOGENEOUS LAYERS .1. MATHEMATICAL FOUNDATIONS

A systems theory describing signal transmission in neuronal layer structures is presented. Such structures having the quality of linearity and homogenity can easily be treated by using a multiple Fourier transformation method with respect to the space coordinates and to the time. The characteristic laws of this transformation are discussed. In analogy to linear networks the transfer function, the impulse response function and the step response function are defined which characterizes the layer system. Appropriate test functions are derived. Typical structures of standing and moving patterns are finally discussed. Biological application and simulation of the theory by a system using coherent optics will be presented later. © 1969 Springer-Verlag.