Multistability of Neural Networks with Time-Varying Delays and Concave-Convex Characteristics

作者：Zeng Zhigang^*; Zheng Wei Xing

来源：IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(2): 293-305.

DOI：10.1109/TNNLS.2011.2179311

• Attractive set
• concave-convex characteristics
• fixed point
• multistability
• neural networks
• time-varying delays

In this paper, stability of multiple equilibria of neural networks with time-varying delays and concave-convex characteristics is formulated and studied. Some sufficient conditions are obtained to ensure that an n-neuron neural network with concave-convex characteristics can have a fixed point located in the appointed region. By means of an appropriate partition of the n-dimensional state space, when nonlinear activation functions of an n-neuron neural network are concave or convex in 2k+2m-1 intervals, this neural network can have (2k+2m-1)(n) equilibrium points. This result can be applied to the multiobjective optimal control and associative memory. In particular, several succinct criteria are given to ascertain multistability of cellular neural networks. These stability conditions are the improvement and extension of the existing stability results in the literature. A numerical example is given to illustrate the theoretical findings via computer simulations.

• 出版日期2012-2
• 单位华中科技大学