Research On Synchronous Control Problems Driven By Evolutionary Parameters

Synchronization,as a collective dynamic behavior in complex network systems,is ubiquitous in nature.It has been involved in various fields of various disciplines,from micro to macro,from the huge cosmic bodies,complex power systems,colorful biological populations,to the small individual heart system,complex neural network system,microbial circulation system,etc.The subject of complex systems is full of mysteries to be explored,among which the human brain,as a complex information processing system,is also full of unknowns.The new developments in science and technology have opened up a new way for the continuous exploration of mankind.In recent years,the synchronization of neurons has also been widely studied,which provides deep insight into the understanding of vision,movement,memory,brain disorder.Kuramoto model provides a simple mathematical model of synchronous phenomena,each oscillator has its own intrinsic frequency.The traditional approach of Kuramoto model to achieve synchronization is either by increasing the coupling strength or by increasing the neighborhood size.This thesis mainly studies drive synchronization,where we initialize the coupling strength below the threshold,the system is out of sync;Later we add the external driver with frequency close to the oscillators,they gradually achieve synchronization.We use the Kuramoto model to simulate the thinking mode of human brain.However,there are some differences between the traditional Kuramoto model and human brain,which cannot be directly applied,so we improve the Kuramoto model.We study synchronization of coupled oscillators under weak coupling thresholds(above which global synchronization is achieved,asynchronous otherwise),by adding an external driver to simulate the stimulation of the human brain.This thesis mainly studies a collective behavior of resonance synchronization in heterogeneous networks and puts forward the effect of resonance synchronization mechanism on information retrieval in coded networks.We use improved Kuramoto phase oscillators to simulate normal neurons in a self-oscillating state and investigate the collective response of the fully connected neural network to stimulus signals in a critical state just below the synchronization threshold.Using a resonant frequency driver to stimulate a node can activate an out-of-sync oscillator in the network,locking it in a collective synchronization state similar to its frequency,thus restoring the location of memory through a synchronization pattern associated with a predetermined frequency distribution.The model proposes a potential mechanism to explain how the brain stores and retrieves information from the resonant synchronization pattern.The consciousness of human brain and its memory mechanism are the most fascinating questions in physics and biology.With the help of molecular biology and brain magnetic resonance imaging(MRI),neurobiologists have clarified the physical structure and functions of neurons in certain functional areas.The cerebral cortex has been shown to be a complex network of well-connected neurons in a critical state,firing synchronously when stimulated by a certain stimulus source.Since the synchronous mode of neurons is involved in cognitive activities,different mathematical models are proposed to understand the conscious activities at different spatial and temporal scales.However,due to the complexity of neural networks,the collective behavior(whole-brain dynamics)of these multi-agent systems is unknown and no effective analytical method is available.Most dynamical simulations can only give the macroscopic properties of steady-state behavior or the anomalous dynamics of neural activity.Based on the synchronous spatio-temporal model in large-scale brain activity,we adopt the Kuramoto network model,which is a typical microscopic model of globally coupled nonlinear oscillators,to study the collective dynamics of oscillators under the condition of self-excited oscillation by introducing time-varying driving forces.In order to study the perturbation propagation and pinning control in continuous harmonic driven networks,many similar works have been done.However,our research focuses on another aspect of the driver problem,finding that the Kuramoto network exhibits an enhanced synchronization that enables information retrieval in heterogeneous critical networks through resonance stimuli.By studying the synchronization and Pearson correlation coefficients of the Kuramoto network,we find that when the coupling strength between the Kuramoto oscillators is slightly lower than the synchronization threshold,the coupled driver will synchronize the oscillators with similar frequencies in the network.As we point out,resonant synchronization may be a potential mechanism for memory encoding and retrieval.In the first chapter,we briefly introduce the related knowledge of complex systems,synchronization,and the state-of-the-art of driving synchronization.In chapter 2,the classical dynamics of Kuramoto model is introduced in detail,where the order parameter and average field theory,the analytic method of high dimensional coupling system are reviewed.In chapter 3,the synchronization of neural Kuramoto model driven by parameters is studied in detail.The Kuramoto model of human neural network,timevarying frequency and coupling intensity are proposed.Secondly,the synchronization dynamics driven by parameters is studied.Finally,resonance synchronization and information extraction are observed through numerical simulations.In chapter 4,we consider the quantum synchronization behavior of Lohe model,study the responses of quantum synchronization models in different dimensions to the coupling intensity and number of particles,and extend the idea of resonance synchronization to the quantum level in higher dimensions.