Prediction And Synchronization Of Real Chaotic Systems Based On Echo-state Networks

Synchrony is a common collective dynamic behavior in nature and has been paid attention by researchers in different fields of science.The synchronization behavior of chaotic oscillators and the improvement of synchronization performance by different means are also hot topics.With the rapid development of machine learning and artificial intelligence,our computing power of software and hardware has been enhanced.Using machine learning to replace mathematical models for relevant sequence prediction,synchronous research and the research on the internal memory mode or mechanism of learning machines have also attracted the attention of scholars in different fields.In this paper,we mainly discuss and study the synchronization behavior of chaotic oscillator in three levels:study on periodic coupling mode in mathematical model,study on machine learning for coupling synchronization of training simulation data,and study on machine learning for coupling synchronization of training experimental data.The chapter one is the introduction.We first introduce the knowledge and background of chaotic synchronization and the simulation model of training data by machine.We will briefly review the basic concepts of chaotic oscillators,the synchronization of chaotic models,and some of the effective methods for determining chaos,such as the lyapunov exponential analysis method and the method for determining the stability of models,namely the Master Stability Function analysis method.In chapter two,we introduce the concepts and knowledge of periodic coupling and theoretical analysis.This paper studies how to improve the synchronization performance of the system through periodic coupling and introduces the concept of on-off coupling similar to periodic coupling.We study the synchronization of two chaotic oscillators by using the switch coupling similar to the pulse form,mainly discuss the effect of pulse width and frequency on the synchronization performance,and find some interesting results.We took a single-channel one-way coupling,which was done to keep the coupling consistent with the machine learning synchronization that followed.We find that the selected coupling oscillator is simulated in the way described above,the improvement of synchronization performance is related to the pulse width and frequency of the coupling signal,and there are optimized parameters in a small range,which are one to two orders of magnitude more error than the direct coupling mode.In chapter three,we introduce machine learning algorithms.Firstly,the background knowledge of machine learning is introduced,as well as the details and improvements of esn algorithm we use,especially the meanings and adjustment methods of various super parameters that affect the learning effect.Numerical simulation and calculation are carried out at three levels:First,through direct simulation of the ODE equation,we found that the pulse width and frequency of the coupled signal have an impact on the synchronization performance,and there is a region of optimized values,and the coupling strength needs to be given an appropriate fixed value.Secondly,we will use the machine learning model(ESN)to replace the simulated data into a transmitter model that can emit signals,and we can find a similar phenomenon through experiments.Third,we directly conducted the same experiment with the experimental data obtained through the relevant channels,and found similar effects and the same conclusions.However,due to the inevitable random errors in the experimental data,the results may be slightly different,but the regions are generally similar.Finally,through the observed phenomenon and the observed experimental results,it can be concluded that under certain coupling strength,our model can improve signal synchronization performance by changing the coupling data pulse width and frequency,and incomplete signal data coupling has better synchronization performance than direct coupling.The practical significance is that we can carry out signal restoration and reconstruction through such ESN-like model,because the machine itself has memory function.In the chapter four,we summarize and look forward to the work we have done.