Research On Dynamical Behaviors Of Complex Systems

Since the researches on complexity quickly progress,the methodology of complex systems has developed some successful models and arithmetic.This thesis studies the dynamical behaviors of a number of complex systems related to communication,socioeconomics and physiology based on the developed methodology of complex system.To begin with we investigate the dynamical behaviors of Internet because it is a typical example of communication system as well as a complex system.The current research on Internet including the topology dynamics and developed topology generator has been introduced.Then,the traffic in Internet considered as point process is analyzed by statistical methods.The empirical results suggest that the data have a symmetry heavy-tailed distribution,with the corresponding cumulative distributions of both negative and positive tails can be well fitted by a L(?)vy regime or an extendedly asymptotic power-law form.In further,the investigation of long-range dependence of the absolute value of both packet-changes and byte-changes by using the detrended fluctuation analysis demonstrates the presentence of memory which distinguishes the evolution of traffic with the general Poisson process.After the empirical studies on the dynamics of Internet, a artificial traffic model based on scale-free networks is proposed to mimic the intrinsic mechanism and congestion control of traffic.Instead of using the routing strategy of the shortest path,a generalized routing algorithm is introduced to improve the transportation throughput,which is measured by the value of the critical point disjoining the free-flow phase and the congested phase.By using the detrended fluctuation analysis,we find that the traffic near the critical point exhibits the 1/f -type scaling in the power spectrum which suggests the system relates to self-organized system.Second,the dynamical characteristics of financial markets are presented by analyzing the price fluctuation.The similarities and differences of stylized-facts and scaling behaviors of financial markets are in detail investigated.Compared the empirical results of emerging financial markets with that of developed financial markets,the distributions of return of Shanghai synthetic index and Hang Sang index in Hong Kong have much sharper peak and fatter tail.The scaling behaviors include self-similar long-range power-law behavior,multi-fractal and diffusion entropy scale.In particular,the diffusion entropy scales of financial index demonstrate the memory embedding in financial markets.Last but not least we present the investigation on dynamical behaviors of the complex systems related to physiology,which include brain,heart and human gait.First,by using a modified random walk method,it is demonstrated that scale-invariance is embedded in EEG signals after a detrending procedure is applied.Furthermore,we study the dynamical evolution of the probability density function(PDF) of the detrended EEG signals by nonextensive statistical modeling.It displays a scale-independent property, which is markedly different from the usual scale-dependent PDF evolution and can't be described by the Fokker-Planck equation,second,the investigation on a set of complex heart rate time series from healthy human in different behavior states with detrended fluctuation analysis and diffusion entropy method is presented.It is proposed that the scaling properties are influenced by behavior states.The memory detected by diffusion entropy displays an approximately same pattern after a Flourier-transform-based detrending procedure.Third,the diffusion entropy technique is applied to investigate the scaling behaviors of stride interval fluctuations of human gait.The scaling behaviors of the stride interval of human walking at norm,slow,and fast rate are similar.Dynamical analysis of these stride interval fluctuations reveals a self-similar pattern:fluctuation at one time scale are statistically similar to those at multiple other time scales,at least over hundreds of steps,while the healthy subjects walk at their norm rate.These findings suggest that the fractal dynamics of stride interval fluctuation of human gait intrinsic to the locomotor system is different from regular memoryless diffusion process.The studies on the dynamical behaviors of a number of complex systems can help us understand the intrinsic mechanism and provide a insight to construct the models.It is also of importance for seeking the universal rule and developing the methodology of complex systems...