Stochastic fixed-time quantitative synchronization for multilayer derivative dynamic Cohen–Grossberg networks and secure communication

The implementation of fixed-time synchronization is a challenging problem for dynamic networks with derivative coupling. When there are derivative coupling in multilayer heterogeneous dynamic networks, it is difficult to obtain the fixed-time stable synchronization criteria via using the conventional Lyapunov function. To overcome these difficulty and challenge, we choose a special Lyapunov function to solve the fixed-time stable synchronization criteria. To eliminate the differential term in fixed time controller and reduce the difficulty of the design for controller, different from the comprehensive method used in lots of literatures, we use analysis method to design a fixed time control strategy. To be closer to reality, we consider multilayer neural networks with stochastic disturbances and nonlinear connections. When designing the controller, considering the actual communication constraints, we introduce quantization into the designed controller. Under the theoretical framework, we find that the upper limit for function of synchronization time is related to the quantization intensity, parameters of the designed Lyapunov function, parameters of the controller and a maximum eigenvalue related to the structure of multilayer Cohen–Grossberg neural networks. Finally, an secure communication algorithm based on the synchronization scheme is designed. The secure communication algorithm can be achieved before 11.0027. This shows that the derived theoretical framework is effective.