Interval Bipartite Synchronization of Delayed Nonlinear Neural Networks With Signed Graphs

The cooperation of linear multiagent systems (MASs) in the signed graphs has received wide attention. However, time delays and nonlinearity are ignored. This article deals with the cooperation behavior, especially interval bipartite synchronization (IBS) of delayed nonlinear neural networks (NNs) with signed graphs. A generalized matrix is proposed for the construction of the Lyapunov functionals, establishing sufficient conditions in a linear matrix inequality related to the coupling strength, the delays, and the network structure. It suggests that the negative rooted cycles and the negative nonrooted cycles take an important part in stabilizing delayed nonlinear NNs and leading to their diversity, and time delays, especially communication delays, significantly impact cooperation performance. Numerical examples are employed to validate our derived results.