Structures And Dynamics In Complex Systems

The period from the end of the 20th century to the beginning of the 21st cen-tury is the spring of complexity science and complex systems research.At that time,when the computing technology was becoming mature and popular,the re-search paradigm of numerical calculation and simulation brought a period of vig-orous development for the study of complex systems.In recent years,the rapid rise of data science is setting off a new revolution in the scientific research paradigm,namely data-driven research,which has a particularly significant impact on the field of complex systems research.However,as data-driven research represented by machine learning methods such as deep neural networks(DNN)has begun to evolve from a frenzy in the period of rapid development to mature and rational thinking,people have gradually realized its common disadvantages such as lack of interpretability,transferability,etc.For many complex system research problems in reality,it is difficult to meet the needs of practical problems only by theoretical models,and it is difficult to go deep into the extraction of universal knowledge by data learning alone.Therefore,the research paradigm that combines model hypothesis and data learning has its special significance for the study of complex systems.The research in this Ph.D thesis is mainly to develop and explore the rele-vant theoretical and technical methods for studying the structure and dynamics in complex systems based on the "model+data" research paradigm.Specifically,we(1)developed a compressed sensing optimization method for sparse struc-ture detection and dynamic equation reconstruction in complex systems,and pre-sented a scalable theoretical analysis framework.We also applied it to the detec-tion of hidden interactions in active body sysytems,reconstruction of brain func-tional networks,and fitting of dynamical equations;(2)developed a novel net-work percolation dynamical model based on neurophysiological findings,reveal-ing the neurodynamic mechanism behind the“hysteresis phenomenon" commonly observed in clinical anesthesia and experiments;(3)discovered some features of the resting-state functional structures of the human brain's default mode network by the compressed sensing based partial correlation and convergent cross mapping methods,and obtained some new cognitive neuroscience conclusions;(4)analyzed the resting-state energy landscape of the human brain's default mode network and revealed the correspondence between the metastable basins in the energy landscape and the states of neural activity in the visual and auditory cortex,which deepens the understanding of the resting-state dynamics of the default mode network.These studies are typical examples of studying the structure and dynamics of complex systems by combining models and methods in the fields of statistical physics,nonlinear dynamics,and complex networks with observations or mea-surements for specific systems.The corresponding results not only have scientific and application value for the study of specific systems themselves,but also have a heuristic significance in the methodology of complex systems research.