Generalized and Exponential Synchronization for a Class of Novel Complex Dynamic Networks with Hybrid Time-varying Delay via IPAPC

Abstract

This paper introduced a new class of Complex Dynamic Networks (CDNs) with hybrid Time-Varying Delay (TVD) and Non-Time-Varying Delay (NTVD) nodes. Exponential Synchronization (ES) and Generalized Synchronization(GS) problems are studied by using a novel coupling Intermittent Periodically Adaptive Pinning Control (IPAPC) with these CDNs. Meanwhile, IPAPC has new characteristics with three switched intervals in every period. Based on IPAPC method, Kronecker product rules and Lyapunov Stability Theory (LST), necessary and sufficient conditions for ES and GS with IPAPC criteria of such CDNs have been deduced theoretically. Moreover, to verify the practicability and effectiveness of the proposed theoretical results and method, Nearest-Neighbor Network (NNN) and Barabasi-Albert Network (BAN) consisting of coupled delay and non-delayed Lee chaotic attractor are finally given as the examples.