Uncertainty quantification of exponential synchronization for a novel class of complex dynamical networks with hybrid TVD using PIPC

This paper investigates the Uncertainty Quantification (UQ) of Exponential Synchronization (ES) problems for a new class of Complex Dynamical Networks (CDNs) with hybrid Time-Varying Delay (TVD) and Non-Time-Varying Delay (NTVD) nodes by using coupling Periodically Intermittent Pinning Control (PIPC) which has three switched intervals in every period. Based on Kronecker product rules, Lyapunov Stability Theory (LST), Cumulative Distribution Function (CDF), and PIPC method, the robustness of the control algorithm with respect to the value of the final time is studied. Moreover, we assume a normal distribution for the time and used the Stochastic Collocation (SC) method [1] with different values of nodes and collocation points to quantify the sensitivity. For different numbers of nodes, the results show that the ES errors converge to zero with a high probability. Finally, to verify the effectiveness of our theoretical results, Nearest-Neighbor Network (NNN) and Barabási-Albert Network (BAN) consisting of coupled non-delayed and delay Chen oscillators are studied and to demonstrate that the accuracies of the ES and PIPC are robust to variations of time.