The multistability of delayed competitive neural networks with piecewise non-monotonic activation functions

This paper addresses the problem of multistability of competitive neural networks with nonlinear, non-monotonic piecewise activation functions and time-varying delays. Several sufficient conditions are proposed to guarantee the existence of (2K+1)(n) equilibrium points and the locally exponential stability of (K+1)(n) equilibrium points, where K is a positive integer and determined by the property of activation functions and the parameters of neural networks. The quantitative relationship between the equilibrium points of the system and the zero roots of the bounding functions is given. In addition, the attraction basins of the exponentially stable equilibrium points are obtained. Finally, a numerical simulation is given to illustrate the effectiveness of the obtained results.