Models of Complex-Valued Dynamic Associative Memories and Analysis of Their Dynamics - Analytic and Non-analytic Activation Functions

Associative memories are one of the popular applications of neural networks and several studies on their extension to the complex domain have been done. Associative memories should recall memory patterns, and their dynamics are greatly affected by activation functions and connection weights. The theoretical analysis on qualitative properties of neural networks is very important to associative memories. We already proposed some models of complex valued associative memory using nonlinear bounded complex functions, which are not analytic. In this paper, we present several models of orthogonal type and auto-correlation type associative memories using several nonlinear complex functions which include analytic and non-analytic functions, and investigate their behavior as associative memories theoretically. Comparisons are made among these models in terms of dynamics. Simulation studies are also done to investigate dynamics of an associative memory with singular points.