Stochastic fixed-time synchronization for multilayer derivative dynamic Cohen-Grossberg networks via quantitative control

Abstract

The implementation of fixed-time synchronization is a challenging problem for dynamic networks with derivative links. When there are derivative links in multilayer heterogeneous dynamic networks, it is difficult to obtain the fixedtime stable synchronization criteria via using the conventional Lyapunov function. So we choose a special Lyapunov function to solve the fixed-time stable synchronization criteria. In this paper, different from the comprehensive method used in lots of literature, to design and solve the fixed time controller, we use the analysis method to design a fixed time control strategy. When this strategy is used for the fixed-time synchronization of multilayer Heterogeneous networks with Cohen-Grossberg neural subnet, it will result in the designed controller does not contain differential terms, so as to reduce the difficulty in the design of fixed time controller. 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, a simulation is supported to illustrate the effective of the derived theoretical framework.

Fixed‐time synchronization in multilayer networks with delay Cohen–Grossberg neural subnets via adaptive quantitative control

“…(1) without random external coupling can be fixed-timely synchronized to (3) via the controller (7) and the adaptive updating law (8). Fixed settling time can be calculated by (11).…”

“…Synchronization under neural networks and its application were focused in many works, such as encryption based on synchronization in multilayer neural network in Sarkar [10] and synchronization-based encryption under neural networks in Tan et al [11]. Finite time synchronization has been studied by many researchers.…”

“…Errors e i𝑗 (t).based on Definition 1 and Lemma 2 in probability. Fixed settling time can be estimated by(11). □ Remark 5.…”