Abstract: In recent years, complex networks have attracted the attention of researchers in various fields of science and engineering, and become a research hotspot. In this paper, the stability analysis theory, control theory and matrix theory of time-delay systems are applied to complex networks, and the modeling and synchronous dynamics characteristics of complex networks are deeply studied. Both theoretical research and practical application are of great significance. Due to the influence of spatial distance (ellipsis) in the actual network, the coupling between node States has time delay. At present, most of the research is aimed at simple time delay coupling, which is only a simplified description of the actual network. A generalized complex network model with mixed delay coupling is proposed, which reflects the characteristics of the actual network more truly and comprehensively, not only considering the coupling between state variables, but also reflecting the change rate of interaction between state variables. Some existing complex network models can be regarded as its special cases, so it is of great academic significance and application value to study this kind of generalized complex network. Furthermore, by analyzing the synchronous dynamic characteristics of complex networks with mixed delays, on the one hand, we can better understand and explain the dynamic nodes of complex networks in the real world, on the other hand, we can design (slightly) good networks according to the theoretical research results of complex network synchronization. The main content and innovation of this paper can be summarized as: 1. A generalized hybrid coupled delay complex network model is proposed. Compared with existing network models, the proposed model considers more general situations, namely ...
In the past ten years, X network has attracted the attention of many disciplines, such as physics, biology, social science, telecommunications and engineering. This paper introduces the stability theory, control theory and matrix theory of time-delay systems in complex networks. Modeling and analysis of complex networks are of great significance in both theoretical development and practical application. Time delay ...
Table of contents: pages 5-7 of the abstract
Page 7-9 of the abstract
Chapter 1 Introduction Page 15-34
? Complex network and its development 15-22 pages
? Research status of complex network synchronization 22-28 pages
? Network parameters affecting synchronization performance Page 23-25
? Methods to improve network synchronization ability Page 25-27
? The application of complex network synchronization 27-28 pages
? Mathematical description of complex network synchronization Page 28-30
? Research significance of synchronization in complex networks with coupling delay
? The structure of this article is on pages 32-34.
In chapter 2, synchronization of a class of generalized coupled time-delay complex networks.
? Introduction Page 34-35
? Model description of generalized time-delay coupled complex networks
? Local Synchronization Page 38-48
? Model transformation Page 38-39
? Delay-independent local synchronization standard Page 39-40
? Delay-related local synchronization standards Page 40-44
? Numerical Simulation Page 44-48
? Global Synchronization Page 48-56
? Model transformation Page 49-50
? Delay-related global synchronization standards Page 50-53
? Delay-independent global synchronization standard Page 53-54
? Numerical Simulation Page 54-56
? Page 56-57 of this chapter's summary
Chapter 3 Exponential Synchronization of Generalized Coupled Complex Networks with Time Delay
? Introduction Page 57-58
? Model Description and Preparatory Knowledge Page 58-59
? Synchronous analysis and index estimation 59-66
? Model transformation page 59-60
? Delay-related exponential synchronization standard 60-66 pages
? Numerical Simulation Page 66-69
? Page 69-70 of this chapter's abstract
Chapter 4 Synchronization of Coupled Time-delay Complex Networks Based on Impulse Control 70-88