英文摘要： Since time delay is common and ubiquitous in real coupled systems, the dynamics of nonlinear coupled systems with time delays has attracted considerable attention and become a frontier research topic. This project focuses on various dynamical behaviors of nonlinear coupled systems with time delays. The main themes and contributions of the project include: The dynamical models are presented based on the characteristics of real coupled systems. The simple stability criteria of coupled systems are proposed and the influences of multiple time delays on the stability of coupled systems are discussed. The conditions of different bifurcations when the coupled system loses its stability locally are derived. New qualitative and quantitate methods are developed to determine the dynamical characteristics of bifurcation points. The high codimensional bifurcations and complex behaviors due to time delays and couplings are explored. Synchronization and its transitions of coupled systems are investigated. The effects of time delays on the existence and switches of different synchronization phenomena are given. The platform of circuit experiments for the nonlinear coupled systems with time delays is designed and can be used to show various properties of the coupled systems under different parameters. The results of theoretical analysis and numerical simulations can be validated through circuit experiments. The aims and objectives of the research are to develop novel and effective theoretical methods, efficient and general numerical algorithms, and high precision real-time experimental technology, reveal the mechanisms of complex dynamical behaviors due to time delays, and promote the application and development of the nonlinear dynamics of time-delayed systems.
英文关键词： time delay;coupled systems;nonlinear oscillations;complex dynamics;circuit experiment