Global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations

In this paper, we investigate the global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations. Employing the Leray–Schauder alternative theorem in multivalued analysis, linear matrix inequality technique and generalized Lyapunov-like method, we obtain some new sufficient conditions ensuring the existence, uniqueness and global stability and the global convergence in finite time of the equilibrium point, the results of this paper improve and extend previously known results. Finally, two examples and numerical simulations are conducted to validate the theoretical results.