Multistability of Cohen-Grossberg neural networks based on activation functions with multiple discontinuous points

This paper studies multistability of Cohen-Grossberg neural networks (CGNNs) with a kind of discontinuous activation function (AF), which has multiple discontinuous points. Under some criteria, CGNNs with the discontinuous AF designed in this paper can produce (4k+1)n equilibrium points (EPs), therein (3k+1)n EPs are located at the continuous points in the AF and (2k + 1)n EPs are locally exponentially stable. CGNNs with the designed AF can produce even larger quantity of stable/total EPs compared with the AF in existing literature. Therefore, when CGNNs with the designed discontinuous AF are applied to associative memory, they could store more prototype patterns. Moreover, the attraction basins of the stable EPs in CGNNs are estimated and enlarged. A numerical example is illustrated to testify the correctness of the obtained results.