Multistability of Second-Order Competitive Neural Networks With Nondecreasing Saturated Activation Functions

作者：Nie Xiaobing^*; Cao Jinde

来源：IEEE Transactions on Neural Networks, 2011, 22(11): 1694-1708.

DOI：10.1109/TNN.2011.2164934

• Competitive neural networks
• multistability
• saturated activation functions
• second-order interactions

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2(N) equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2 r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)(N) locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

• 出版日期2011-11
• 单位东南大学