On The Research Of Initial Value Sensitive Problem In High Dimensional Complex Dynamic Networks

The theme of the paper is the evolution of complex system. First we discuss twoissues from two different evolution directions, and then do uniformly discussion.Synchronization is an interesting phenomenon showing a complex system’s evolutionfrom simple to complex. The relationship between convergence rate tosynchronization and graph structure behind interactions is one problem which westudy here. In the continuous model it already has a measure of speed of convergence.When we try to extend it to the discrete situation, we give out a better measure, andextend the new measure from non-directed graph to digraphs. Finally we match ourconclusion to the realistic situation and some generalize problem. Chaos is a complexbehavior in system evolution, which is a hotspot problem. We extract out a partproblem of chaos which is initial value sensitive problem to study. We first describethe phenomenon in the model, and then based on the potential function decompositionframework we construct the analytical form of the potential function of the system.On this basis, we first find the analysis methods and the rules from thetwo-dimensional problem, and then extended to the three-dimensional case. Using thesimilar idea combined with the special analysis and calculation, we finally gives outan intuitive explanation of the3D special initial value sensitive problem with tracks’jumping separation phenomenon. Further, we introduce the basis of fractal theory andthen discussed the fractal structure of chaotic attractors, then show its related factorsin the chaotic attractors in the model. Again from chaos to the simple, to discuss thephenomenon of self-organization phenomena linked with the synchronization wediscussed. Then we talk about the butterfly effect with expanding content. Finally, wereturn to the system evolution theme to make a summary of this article. Through thework of this paper, we can find it interesting and meaningful.