Study On The Spatiotemporal Structure And Dynamics Of Complex Systems

Since the turn of the century,researchers have focused on complex systems and networks.Due to its relevance to human civilization and nature,complexity science has gained a lot of interest as a cutting-edge interdisciplinary field.However,due to the numerous components and intricate interactions of complex systems,it is difficult to precisely determine the initial conditions of evolution and formulate an equation that can adequately represent the dynamic behavior of these systems.Therefore,using conventional reductionist methods to describe and simulate complex systems is impossible.Physics offers a natural edge in solving these issues in complex dynamical systems,particularly statistical physics methods.There is now enough historical data available thanks to the advancement of digital technology.To examine the spatiotemporal structure of complex systems and the fundamental principles governing their evolution,physicists have created tools like microscopic interaction models,complex network analysis,and temporal and spatial correlation functions.This essay focuses on the most recent progress and uses of these methods.We use the population migration and financial market systems as our research objects because they are both typical complex systems.We study the dynamical evolution and spatiotemporal structures of these systems.In Chapter 1,we provide a brief overview of the complex systems theory,including the measure of complexity and the essential characteristics of complex systems.Next,we introduce an analytical approach to the spatial structure of complex systems,namely the complex network approach.We also introduce the statistical properties of the time series and dynamics analysis methods in complex systems,including temporal and spatial correlation functions and random matrix theory.Finally,we describe the motivation and innovation of this paper.In Chapter 2,we outline the pertinent research developments on the two complex systems in which this study is interested:population migrations and financial markets.Individual migration behavior is far from random but highly regular and predictable for population migration systems.We review the statistical characteristics of human migration and several important migration models.The financial market,as an ever-evolving complex system,has also attracted the attention of physicists.We briefly review the related research on financial time series’ statistical and dynamic characteristics in financial physics.In Chapter 3,since the China Household Finance Survey(CHFS)fills the gap in the long-term and long-distance migration behavior dataset,based on the CHFS dataset,we consider a dynamically changing population migration system.By introducing the gravity model and community structure detection method,we study the critical influence of economy and geographic location on migration behavior and the community structure of the migration network.We propose an agentbased random walk model for population migration.Through simulations,we examine whether the current system is in a stationary state,and the population distribution when the system evolves to a stationary state.Because they are representative of industrialized nations,the migration patterns for the United Kingdom are noteworthy.On the basis of the UK population migration dataset,our modeling is also confirmed.Furthermore,we extend this model to the migration behavior of individuals with heterogeneous attributes to predict the distribution of individual characteristics across regions.These results are essential for guiding talent policy and industrial layout.The above analysis ideas and modeling methods can also be extended to other real and virtual migration processes of complex systems(such as the Internet,etc.).This method is also applicable to other problems involving multi-body migration,whether the system is in a stationary state or non-stationary state.In Chapter 4,the financial system and its temporal and spatial correlations are very complex.Many correlations and causality between various physical quantities need to be carefully and deeply studied.We innovatively introduce the return-volume correlation as a characteristic quantity and establish the link between the micro-trading behavior of market participants and the macro-variable stock price.We first classify stocks using return-volume correlations.Then we introduce the temporal correlation function to investigate the behavior of the price dynamics.Based on these results,we also discuss applying the return-volume correlation classification method to portfolio optimization problems in both theoretical and practical backtesting.These results enrich the understanding of price dynamics while providing an efficient portfolio optimization approach.In Chapter 5,we summarize the main results of this paper and provide an outlook on the future directions of exploration.