Search Strategy For Complex Network And Numerical Methods For Its Related Models

Complex networks exist in many fields of our life. Search problem has always been one of important research topics in complex network theoretical study. The research of the complex network search strategy is of great significance to the real life. Many networks in the real world are dynamic and stochastic. Complex network search as a basic tool is often used to solve some optimization problems.In this dissertation, we introduce the basic complex network search models and search algorithms, analyze and compare the basic complex network search strategy. The new search method is proposed, the improved search algorithm is validated. On the basis of this, we investigate the numerical methods of complex network search and confirm the theoretical claims. The contributions of this thesis are as follows:Firstly, we discuss the brownian motion and anomalous diffusion phenomenon and study the anomalous diffusion behaviour of particles according to numerical result. We investigate the jump length and waiting time distribution function of continuous time random walk model. According to aging update theory, we study the continuous time random walk model and obtain the aging diffusion equation. The aging diffusion equation can describe the aging dynamic system. At the same time, we study the Fokker-Planck equation, which probability density function is changing with time. The Fokker-Planck equation stability is analyzed. The predictor-corrector approximations are used to solve the fractional Fokker-Planck equation.Secondly, based on the random walk theory, we analyze the spatial and temporal coupling random search and discuss the aging effect of the Lévy walk and numerical implementations. The purpose of this dissertation is to explore the effective search strategy of complex network and improve the search efficiency. Here, according to the classic cuckoo search algorithm, this dissertation proposes a new improved Tempered Lévy Flight search algorithm. Several classic functions test show that the improved algorithm can enhance the precision of its search and speed up the convergence speed of the search algorithm. And the improved search algorithm can adjust the search scope, increase species diversity, enhance the adaptive effect, improve the overall performance of the algorithm. In addition, we widely discuss the practical application of the improved search algorithm. This part is the central content of this dissertation.At last, this dissertation discusses the monte carlo numerical simulation method, the dynamic behavior of complex systems are discussed. A weighed numerical scheme can effectively solve the fractional wave equation in a finite domain is provided. We focus on detailedly discussing the two-sided space fractional wave equations with homogeneous boundary conditions. Additionally, the numerical results confirm that the weighted numerical algorithm is convergent with second order accuracy in both space and time directions for the homogeneous boundary fractional problems. This research result provides the theory basis for the study of complex network search.