General decay synchronization of memristor-based Cohen-Grossberg neural networks with mixed time-delays and discontinuous activations

This paper investigates the general decay synchronization (GDS) of memristor-based Cohen-Grossberg neural networks (MCGNNs) with discontinuous neuron activation functions and mixed time-delays. Based on the concept of Filippov solution and theory of differential inclusion, introducing suitable Lyapunov-Krasovskii functionals and employing useful inequality techniques, some novel criteria ensuring the GDS of considered Cohen-Grossberg neural networks are established via two types of nonlinear controls. In addition, the feasibility of the obtained theoretical results is validated via two numerical examples and their simulations. The polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen the special cases of the GDS. To the authors' knowledge, the results established in the paper are the only available results on the synchronization of neural networks, connecting the three main characteristics, i.e., memristor, discontinuous activation functions and mixed time-delays.