Uncertainty quantification of Group Synchronization and control of a new class of adaptive complex dynamical network with brownian motion and Time-varying Delay

This paper investigates the Uncertainty Quantification (UQ) of Group Mean Square Synchronization (GMSS) for a new class of Complex Dynamical Network (CDN) with interval Time-varying Delays (TVD) and Limited Stochastic Perturbation (LSP). Based on the control theory and Stochastic Collocation (SC) method, we have studied the robustness of the control algorithm with respect to the value of the final time. To that end, we assumed a normal distribution for time and used the SC method [1] with different values of nodes n collocation points Ti to quantify the sensitivity. These results show that the synchronization errors are close to zero with a high probability and confirm for different number of nodes. Finally, some examples with different structure chaotic systems and their numerical simulation results are presented to demonstrate the theoretical analysis. Therefore, the conclusion of this study is that the accuracy of the synchronization and control algorithm is robust to variations of time.