Research On Using Reservoir Computing To Reconstruct Attractor And Coupling Mechanism Between Reservoir Computers

The chaotic dynamic system is a kind of system that is extremely sensitive to the initial state,and it has always been a hot and difficult problem about the prediction of the time series and the reconstruction of the chaotic system in this field.In recent years,the rapid development of machine learning technology provides a new idea for the study of chaotic dynamic systems.In particular,the technique known as reservoir computing has attracted more and more attention due to its simple model,easy training and suitable for time series forecasting,and has become a new research hotspot.Furthermore,the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active research since the early days of physics.This paper will study how to use the technology of reservoir computing to reconstruct the chaotic attractors and explore the coupling mechanism and synchronization between the reservoir computers that simulate the chaotic attractor.Previous studies have shown that chaotic oscillators can achieve synchronization through coupling,and can exhibit different synchronization types,such as complete synchronization,phase synchronization,and generalized synchronization.Besides,the research on the reservoir computing shows that it can approximate the asymptotic dynamics of chaotic attractors.Further,we use the R?ssler system and the Lorenz system to conduct experiments,and reconstruct the chaotic system with the method of reservoir computing.Afterwards,inspired by the diffusion coupling between chaotic oscillators,we propose a coupling method between reservoir computers which allows the output of one reservoir computer to be partially fed back to the input layer of the other reservoir computer.In this way,the outputs of two reservoir computers are mixed.The coupling strength represents the proportion of the output fed back to the input of the other reservoir computerThe results of the numerical simulations show that by changing the coupling strength,different types of synchronization can be achieved between the reservoir computers,and under a suitable coupling strength,they can achieve the complete synchronization.