摘要
Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation flmctions 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 flmctions 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.
基金
Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 61034005, and 61074073)
the National Basic Research Program of China (Grant No. 2009CB320601)
the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-10-0306)
the Fundamental Research Funds for the Central Universities of China(Grant Nos. N110604005 and N110504001)
