Multistability of complex-valued neural networks with discontinuous activation functions

In this paper, based on the geometrical properties of the discontinuous activation functions and the Brouwer's fixed point theory, the multistability issue is tackled for the complex-valued neural networks with discontinuous activation functions and time-varying delays. To address the network with discontinuous functions, Filippov solution of the system is defined. Through rigorous analysis, several sufficient criteria are obtained to assure the existence of 25n equilibrium points. Among them, 9n points are locally stable and 16n−9n equilibrium points are unstable. Furthermore, to enlarge the attraction basins of the 9n equilibrium points, some mild conditions are imposed. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.