Non-stationary Temporal-spatial Correlations Of Complex Dynamic Systems And Their Applications

Investigation on the complex dynamic systems has attracted much attention from researchers in different fields,including physicists.For physicists,the dynamic properties of a system in the equilibrium or stationary state can be characterized by temporal-spatial correlation functions.However,dynamic systems in the real world,due to the complexity of their interactions within themselves and with the environment,usually exhibit a series of non-stationary characteristics.Complex systems are thus located far away from the stationary state.Correspondingly,the compu-tation of the temporal-spatial correlation functions will be hindered by the non-stationary dynamic effect.Most of the temporal correlation functions will be around zero or very weak if this non-stationary effect is not considered,and the evolution of spatial correlations over time will be very unstable.Therefore,the main purpose of this paper is to explore how to compute the temporal-spatial correlation functions of complex systems by considering the non-stationary dynamic effect.The underlying mechanism of the non-stationary dynamic effect is investigated by microscopic modelling,which provide new insights for controlling and predicting the behavior of the systems.Complex networks provide a common framework for abstracting and describing different types of complex systems,which helps a lot to reveal the general laws in them.Based on the researches of the topological structures of complex networks,how the network structure affects the dynamic process on it and further influences the function of the system has become one of the most attracting topics in recent years.Previous research shows that the coupling structure of a complex network has a great influence on the robustness of its functions and the way it responds to external disturbances.The exploration of this problem will be helpful to understand the interaction mechanism between the network structure and its functions,and the dynamic evolution process on the network.Taking complex financial network as an example,we study the stability of the network topology evolving with time by introducing the random matrix theory.In Chapter 1,we present a brief introduction to the characteristics of complex systems,fo-cusing on the non-stationary properties,and display several common methods processing the non-stationary time series.Complex networks are introduced to describe the spatial correlation struc-ture of complex systems.The progress of researches related to network topology and its dynamic stability is summarized.Finally,the main motivations and contents of this paper are given.In Chapter 2,we propose a general method for calculating the temporal correlation function of complex dynamic systems away from the stationary state.One of the manifestations of the non-stationary effect of complex systems is the long-range autocorrelation of dynamic fluctuations,which indicates that the dynamic fluctuation will evolve with time even has been averaged over a relatively long time scale,and the existence of this non-stationary effect interferes the computation of the temporal correlation function.Taking the financial,social,biological and ecological systems as examples,the results show that the fluctuations of the systems have a driving effect on its dy-namic variables after taking into account the non-stationary effect.The reliability of this driving mechanism is illustrated in the new framework of the transfer entropy analysis combined with the microscopic modelling.In Chapter 3,we provide an example in the stock market concerning the application of the fluctuation-driving effect revealed in Chapter 2.It is shown that the result can be established in a wide range of complex financial systems.We study the impact of market conditions on this effect by constructing a fluctuation-driven based strategy.Further,the performance of the trading strategy is compared with other technical trading rules.It is proved that the fluctuation-driving effect not only has the theoretical value but also the practical implications.In Chapter 4,we study the spatial structure of complex financial systems by introducing meth-ods of complex networks combined with the random matrix theory.It is discovered that the market mode characterizes the structural stability of the complex systems.The market mode represents the global interactions between different stocks in the market,and our results are robust for both the Chinese and US stock markets.We construct optimal portfolios based on the topological proper-ties of the network nodes,which proves that the stability of the network structure has a significant impact on its function.In Chapter 5,we summarize the main results in this paper and look forward to some possible future directions of our research.