Dynamic Evolution And Functional Modules Of Complex Networks

Functional modules of complex networks play an important role in understanding the structure and function of complex systems.In this thesis,the dynamic evolution mechanism and functional modules of complex networks are investigated by symbolic dynamic system and automata principle,and the obtained results are applied to analyze the regulatory role of network motifs in biological networks.Furthermore,the functional modules is applied to determine the Davenport constant of multiplicative semi-group of polynomial ring over any finite fields,which partially solve an open problem associated with the Davenport constant for semigroups.Consequently,the works of this thesis will help deeply to understanding of the structural mode and evolution mechanism of complex systems,and it's of both important scientific significance and potential applications value.The main contributions of this thesis are summarized as follows:1.Complex networks and their functional modules based on symbolic dynamics and automata principle.On the basis of symbolic dynamics combination with automata principle,the concepts and definitions of the complex networks and their functional modules are proposed.In addition,the evolution process of two dimensions in time and space is analyzed,and the obtained results is used to illustrate correctness of the proposed functional module concepts are verified by the application of classical cyclic groups and the boolean networks.2.Motif structure and,its regulatory function in biolog'ical networks.As a typical functional module in complex biological networks,network motifs play an important regulatory role in biological networks.From the view of the functional modules feather of boolean networks,some kind of typical network motifs are analyzed,and then the regulation mode of biological network in the process of evolution is clarified.3.Determination of Davenport constants of multiplicative semigroups on quotient rings of monadic polynomial ring over finite fields.Zero-sum sequence,as a kind of special structure sequence on multiplicative semigroups,is important role in determination of the Davenport constants of semigroup.Researching based on semigroup theory and zero-sum sequence combination with additive number theory,the Davenport constants of semi-groups of quotient rings of monadic polynomial ring over any finite fields is finally given,when p is prime number.