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Qualitative analysis for recurrent neural networks with linear threshold transfer functions

Multistable networks have attracted much interest in recent years, since multistability is of primary importance for some applications of recurrent neural networks where monostability exhibits some restrictions. This paper focuses on the analysis of dynamical property for a class of additive recurrent neural networks with nonsaturating linear threshold transfer functions. A milder condition is derived to guarantee the boundedness and global attractivity of the networks. Dynamical properties of the equilibria of two-dimensional networks are analyzed theoretically, and the relationships between the equilibria features and network parameters (synaptic weights and external inputs) are revealed. In addition, the sufficient and necessary conditions for coexistence of multiple equilibria are obtained, which confirmed the observations in with a cortex-inspired silicon circuit. The results obtained in this paper are applicable to both symmetric and nonsymmetric networks. Simulation examples are used to illustrate the theory developed in this paper.