ABSTRACT
This chapter uses nonlinear system synthesis and identification methods of Volterra-Wiener series expansion to analyze the behavior of the systems. It shows a variational analysis technique to establish the connection between the differential equations describing the network dynamics and the Volterra series directly. The chapter derives temporal and spatial Volterra kernels for a neural network model whose activity is governed by multiplicative lateral inhibition. The nonlinear analysis technique of Volterra-Wiener expansions has been successfully applied to, among others, the analysis of wave propagation in random media, scattering by random surfaces, Brownian motion, theory of turbulence, and biological systems. Study of Wiener-Volterra systems with application to identification and synthesis of physiological systems is done in a text by Marmarelis and Marmarelis. Schetzen (1980) and Rugh (1981) have provided classic treatments of the Volterra-Wiener approach from a system theoretical point of view.
