Evolving Analysis Of Discrete-Time Systemes Based On Complex Networks

There are a mass of complex systems in the world of nature and society. Complex networks are one of useful instruments to describe all kinds of opened complex systems from technology, biology to society. Therefore, people dedicate themselves to the formation mechanism of topological structure and function, the rules of evolution, critical phase and the process of dynamics of complex networks, in order to further research complex systems.In this paper the evolution of complex networks is discussed from two aspects. The main contents are outlined as follows:Firstly, the network itself is changing over time, such as the growth of nodes or edges. Here, on the basis of the two growth characters of BA model, a special growth network is introduced, which is simple but widely used. Its degree distribution is computed through rate equation method and is proved that it obeys power-law form with the exponent 2.Then the discrepancy of macroscopically property between BA and the model is analyzed as a result of the difference of their topological structure. The model will be applied to the network of university attracting talents. Simulations obtained from SPSS and Mat lab show correctness of the mathematical expectation formula and availability of the model.Secondly, the network itself does not change, but there is an impact on each other among the nodes of network. The dynamic processes of the nodes are studied over time. First of all, the corporation competition networks are set up on the basis of the generalized theory of cooperation networks. Correspondingly, a dynamic investment model is established taking into account such factors as nonlinear and multidimensional natures. Lyapunov function and fixed-point analysis are applied to analyze the stability of the synchronous behavior about corporation investment. The results show that it relates to the number of business competitors (or the degree of nodes) as well as stimulating factor. Two-dimensional and three-dimensional systems are taken as examples to specifically verify the former result. As another result, on the condition of different initial investment amount, when the investment balance of similar enterprises can't be kept, the competitiveness of one corporation will rapidly increase, while the other's will dramatically decline. Finally, the adaptive control is applied to two-dimensional discrete-time systems. The control results are explained from the angle of economics, which can be provided beneficial guidance for the investment strategy of enterprise.