Quantized pinning bipartite synchronization of fractional-order coupled reaction–diffusion neural networks with time-varying delays

Neural synchronization not only has a significant theoretical role for understanding brain function, but also is important for artificial neural network development. In this paper, a novel and more general directed signed network model, consisting of a set of fractional reaction–diffusion delay neural networks, is articulated. Moreover, we also consider the coexistence of cooperation and competition as a coupling scheme among neurons, which is a mechanism found in biological neural interactions. By designing a new quantized pinning controller based on depth-first algorithm and logarithmic quantization, the sufficient conditions for the bipartite synchronization of the addressed network are given by using Lyapunov method, inequality technique and Green's formula. In addition, using M-matrix theory, the more applicable bipartite synchronization criteria in the form of low-dimensional linear matrix inequality and the form of network coupling strength threshold are given respectively. This work enriches and improves the previous works. At last, simulation experiments are offered to verify the correctness of our theoretical results.