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

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. (general)