The Study Of Signal Amplification On Network Motifs

The complex network is a fruitful tool for understanding real complex systems.Many of the complex networks have been shown to share global statistical features including the property of small world and scale-free with different local ones.Intensive statistical studies have revealed that a large number of complex network contain some significantly recurring subgraphs,termed ‘network motif,' which are believed to reflect the local feature of networks and be basic building blocks of these networks.Since motifs are important units on realizing the function of networks,we study weak signal transmission in three-node motif consisting of three bitable nodes and find that such motifs can amplified weak signal.The main research content is as follows:The first chapter is an introduction.In this section,the development of signal amplification and our works are summarized.In the second chapter,the concept of motif are be introduced and the stability of the dynamic model and typical bifurcation are analyzed by modern nonlinear theory.Furthermore,it provides some typical dynamical equations.In the third chapter,we show that the signal amplification can be further enhanced by adding a link between the two input nodes in the feed-forward motif,i.e.,coupled feed-forward motif.We further reveal that the coupling strength of the link regulates the enhancement of signal amplification in the coupled feed-forward motif.We finally analyze the mechanism of signal amplification of such simple structure.In the fourth chapter,we study the signal amplification in the feedback motif which is added a mutual link between two input nodes and output nodes in the feed-forward motif.We find that feedback motif can improve response to weak signal if the output node has a certain degree of feedback to the input nodes.At last,a physical theory is formulated to explain the mechanism of signal amplification.The fifth chapter summarizes the thesis and gives an outlook of the future study.