Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory

Research on Problems of Synchronization of Complex Network Based on Quorum-Sensing in Biological Systems

Author CaoZuo
Tutor ZhangRong
School Jiangnan University
Course Applied Mathematics
Keywords complex dynamical network quorum sensing quorum sensing strength time-delay systems Lyapunoy stability theory complete synchronization
CLC O157.5
Type Master's thesis
Year 2012
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Nonlinear science is applied in many fields, has been extensive attention and research by scientists for a long time. Complex network combined by the nonlinear science and network is also of concern. Its complex structure and dynamic behavior are the focus for researchers, and the synchronization control problem of complex network which in it is an important research topic for scholars.At first, this article make a brief introduction for chaotic concept, synchronization and control method of chaos, delay systems, description and performance of complexity of the complex network, classification of the complex network and so on. Next, study synchronization problem of a new complex network and full synchronization problem of delay complex networks, specific studies are summarized as follows:(1) A new complex network is constructed according to the idea of quorum sensing in biological systems, there is no direct coupling between the nodes, but it is linked by the way of the sense between external signal and nodes. In the periodic boundary conditions, it is proved right based on Lyapunov stability theory that each node movement of the complex network can achieve complete synchronization under certain conditions. The numerical simulation shows the correctness of the results.(2) Construct a complex network with time-delay according to the idea of quorum sensing, apply Lyapunov stability theory to prove that the complete synchronization of node movement of network can achieve by controlling the flux density when system parameters satisfy certain conditions. The numerical simulation results show that the synchronization is available at periodic solutions and complexity of the periodic solutions is not the same with the different quorum sensing strength.

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