Stability and attractive basins of multiple equilibria in delayed two-neuron networks

• 作 者: 黄玉娇 张化光 王占山
• 机 构: College of Information Science and Engineering, Northeastern University,
• 出 处: Chinese Physics B
• 发表日期: 2012年07期
• 关键词: equilibria attractive unstable invariant exponentially decomposing corner illust

Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r(r≥1) corner points is studied. Sufficient conditions are established for checking the existence of (2r+1)2 equilibria in delayed recurrent neural networks. Under these conditions, (r+1)2 equilibria are locally exponentially stable, and (2r+1)2-(r+1)2-r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.

Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r ≥ 1) corner points is studied. Sufficient conditions are established for checking the existence of (2r + 1) 2 equilibria in delayed recurrent neural networks. Under These conditions, (r + 1) 2 equilibria are locally exponentially stable, and (2r + 1) 2- (r + 1) 2-r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.