Non-stationary Temporal Correlation Functions And Information Driving Forces Of Dynamic Systems

In recent years,physicists have become increasingly interested in the research of complex dy-namic systems.Complex dynamic systems may usually be non-stationary,or at least with features of non-stationary states.In the stationary(or equilibrium)state of a dynamic system,dynamic behaviors can be described by temporal and spatial correlation functions of the dynamic variables and fluctuations.In a large class of dynamic systems,however,most temporal correlations are zero or very weak if the dynamic effects of the non-stationary states are not considered.Computations of the temporal and spacial correlation functions are essentially hindered by the dynamic effects of the non-stationary states.Therefore,it is very important to develop methods to compute the cor-relation functions taking into account the non-stationary effects.This is the main purpose of this paper,with focus on the temporal correlation between the past fluctuation and the future motion of the dynamic variables.External forces are an important factor which drive the systems to non-stationary states.Open complex systems are many-body systems whose interplay with the external environment should not be ignored.It is well known in physics that the external force plays a crucial role in dealing with the open systems.As an important example of open complex systems,the financial market is substantially influenced by the external information.However,our understanding of the external information and its controlling effects in the agent-based modeling is still limited.On the other hand,it is rather challenging in the laboratory to capture the statistical features of the financial system only with the internal interactions.This may be due to the small number of experimental subjects.Thus the external information shows its very importance in the human experiments.In recent years,The massive new data sources resulting from human interactions with the Internet offer a better understanding of the profound influence of the external information on the complex financial system.Based on the large-scale data in the public media and stock markets,we first define an information driving force,and analyze how it affects the complex financial system.As an application,we then propose an agent-based model driven by the information driving force.Based on historical big data and with methods in statistical physics,we investigate the sta-tistical properties of complex dynamic systems.The key point is to develop methods to compute the temporal correlation functions in non-stationary states,and agent-based models with external information driving forces.In Chapter 1,we briefly introduced the characteristics of various types of complex dynamic systems,focusing on fluctuations,correlation functions,non-stationary state characteristics,and external forces.Further,we reviewed several types of complex dynamical systems and reviewed some research works in recent years.Finally,we present the research motivation and research content of this paper.In Chapter 2,we propose novel methods to compute the temporal correlation functions of dynamic systems in non-stationary states.which can be applied to any dynamic systems in similar non-stationary states,and can be also extended to the computations of general temporal and spatial correlation functions.The auto-correlation of the dynamic fluctuations is rather strong in a large class of complex dynamic systems.In other words,the dynamic fluctuation averaged even in a large time scale changes with time significantly.This phenomenon actually is a characteristic of the non-stationary states.If the dynamic system is in a sort of time-dependent steady states or not too far from the stationary state,one may still expect to compute the temporal and spatial correlations.After taking into account the dynamic effects of the non-stationary states,we compute new temporal correlation functions.In various dynamic systems,for example,the social,biological and ecological systems,we detect that the past dynamic fluctuations drive the future motion of the dynamic variables.This dynamic effect of the non-stationary states is a robust,intrinsic and important property of the complex dynamic systems.As important examples,we study the social,human brain and atmospheric systems.Chapter 3,Based on the large-scale data in the public media and stock markets,we first define an information driving force,and analyze how it affects the complex financial system.The information driving force is observed to be asymmetric in the bull and bear market states.As an application,we then propose an agent-based model driven by the information driving force.Especially,all the key parameters are determined from the empirical analysis rather than from statistical fitting of the simulation results.With our model,both the stationary properties and non-stationary dynamic behaviors are simulated.Considering the mean-field effect of the external information,we also propose a few-body model to simulate the financial market in the laboratory.Chapter 4,we summarize the main results of the paper and the future work is prospected.