Nonlinear analysis: mathematical theory and biological applications

Wiener's method of a nonlinear system analysis and its application to neurophysiology are surveyed. His theory is explained on the orthogonal functional series expansion of a nonlinear noise with respect to the Brownian motion whose formal derivative is understood as the white Gaussian noise. Then, efforts made for applying the method to practice are discussed. Special attention is paid on relationship between the internal structure of a given nonlinear system and its kernels of the functionals. This serves to explain a meaning of the kernels. Finally, following the works of one of the authors (K-I.N.) and his colleagues, the analysis of the catfish retinal neuron system is introduced as a typical and successful example of the applications in neurophysiology.