Switching analysis of 2-D neural networks with nonsaturating linear threshold transfer functions

Multistable neural networks have attracted much interesting in recent years, since the monostable networks are computationally restricted. Several papers have been proposed to study the dynamical behavior of a class of neural networks with nonsaturating linear threshold transfer functions, in which multiple equilibria can coexist. But much of those methods belong to a static category, which does not consider the behavior arising from the switching of different partitions. This paper focuses on the analysis of the network's behavior when those switching arising from one partition to another dynamically. The contributions of this paper are: (1) Dynamical properties of the equilibria of two-dimensional networks are analyzed theoretically. (2) It proves by mathematics that the given conditions can drive the network (two-dimensional) converging to the different global stable stationary points, or the different multistable stationary points. (3) Digital computer simulations are carried out to validate the performance of our theory findings.