Non-stationary Dynamics Of Complex Systems And Their Applications

Complex dynamic systems are composed of a huge number of complex interacting components,covering a wide range of physical,ecological,and social systems.However,the equations of motion for complex dynamic systems are usually unknown or difficult to be solved.In the stationary or quasi-stationary state,physicists have adopted temporal-spatio correlation functions to characterize the dynamic behaviors of complex systems.However,complex dynamic systems may usually be non-stationary,or at least with features of non-stationary states.Therefore,computations of temporal-spatio correlation functions might be hindered under the assumption of the stationary state.A large class of temporal-spatio correlations might be zero or very weak if the non-stationary effects are not taken into account.The two-point temporal correlation function between the fluctuation and variation of dynamic systems has been preliminarily studied.However,due to complex many-body interactions and noise disturbances,such a simple correlation can not adequately characterize the dynamic behaviors of complex systems.In general,the multi-point temporal correlations comprehensively characterize the dynamic behaviors and underlying interactions.Computations of the multi-point time correlations are usually much more complicated,and few researches focus on it.Therefore,we attempt to propose a useful method to simplify the calculation of the multi-point temporal correlations for complex dynamic systems in non-stationary states,taking the correlation between the past fluctuation and the future motion of the dynamic variable as an example.The external force is an important factor driving complex systems to be non-stationary states.Physicists usually employ the external force to study open systems interacting with the environment.Based on large-scale historical data,the response of the financial systems to the external forces could be analyzed.In fact,various efforts have been made to investigate the external information in complex financial systems.Since complex financial systems may be non-stationary,it is difficult to characterize the impact of external information on the financial market.For example,the general problem of whether or how the external information drives the price return remains controversial,and such explorations are still at the early stage.Therefore,it is important to implement systematic and comprehensive investigations of information-driven complex financial dynamics.In Chapter 1,we briefly introduce complex dynamic systems,focusing on the non-stationary features of complex dynamic systems,and introducing several analytical methods for nonstationary time series.Then,we emphatically introduce the research progress of econophysics with the temporal-spatio correlation of complex financial systems.Further,we introduce several complex dynamic systems.Finally,we describe the research motivation and content of this paper.In Chapter 2,we generalize the non-stationary temporal correlation functions.Since a simple two-point correlation can not adequately characterize the dynamic behaviors of complex systems,such a correlation function is generalized to a multi-point one,and a useful method is proposed to simplify the computations of the multi-point temporal correlation function.This method is then applied to financial,atmospheric,and biological dynamic systems,and a stronger temporal correlation between the past fluctuation and the future motion of variable is detected,which goes beyond the results of two-point temporal correlation.The multi-point temporal correlation functions are important both theoretically and practically.In Chapter 3,we study information-driven complex financial dynamics.Based on largescale historical data in financial markets,an appropriate sentiment index is introduced to analyze the impact of the external information on the price return in financial markets.In particular,a novel method is proposed to compute the sentiment-return correlation function in which the non-stationary effect of sentiment is taken into account.It reveals a pronounced non-zero correlation between the past sentiment and the future motion of the price return,which goes bey ond the results under the assumption of the stationary state.Further,the calculation of correlation functions is extended to a cross-correlation form,and a stratified structure of cross-correlation functions is observed.With the random matrix theory,the features of the stratified structure are quantitatively analyzed.In Chapter 4,the non-stationary temporal correlation functions explored in Chapters 2 and 3 are applied to financial markets,and two investment strategies are constructed based on the temporal correlations.One explores how the dynamic fluctuation drives the movement of the price return,and another examines how the external information affects the dynamic behaviors of the price return.The investment strategies based on the temporal correlations could be more beneficial and less risky.The results of investment strategies provide the investment guide in the financial markets.In Chapter 5,an agent-based model is constructed with the external information,and a unique asymmetric trading probability is introduced in the model.Such a model successfully simulates the dynamic properties of complex financial systems.In particular,the model parameters are estimated from empirical data rather than artificially set.In Chapter 6,we summarize the main results of this paper,and provide an outlook for the future work.The non-stationary correlation functions lay the basis for constructing the empirical models,as well as investigating multi-degree-of-freedom collective dynamical behaviors and its response to the external forces.In this work,based on statistical physics methods and concepts,the key is to generalize the computations of non-stationary correlation function with historical big data.We mainly focus on two aspects:one is the multi-point correlation function of complex dynamic systems,and the other is the non-stationary dynamics of information-driven force.Finally,the theoretical results are applied to the investment applications in the financial markets.