Prediction Of Chaotic Phase Synchronization By Reservoir Computing

Recently,machine learning has become an important tool for studying model-free prediction of chaotic systems.Among other algorithms,Reservoir Computing(RC)has attracted a lot of attention due to its simple structure and high learning efficiency.A large number of studies have focused on RC in the aspects of its optimization,improvement of performance,as well as applications,and have obtained plenty of achievements.However,it remains not fully solved to train RC to make long-term time series predictions and hence,transitions to different synchronization states.The traditional parameter-aware RC algorithm is only capable of accurately predicting four to five Lyapunov time steps,which does not meet the demand of characterizing phase synchronization under weak coupling.Therefore,we generalize the control parameter-aware reservoir computing.In addition,current research on RC mainly focuses on time series prediction but hardly touches upon classification.Hence,it is necessary to explore how RC plays its role in classification among different chaotic systems.We conduct our research as follows:1.We use conventional RC to predict the dynamics of typical chaotic systems.We apply RC to time series prediction and phase space reconstruction of the Logistic Map,Mackey-Glass,Lorenz,and R?ssler systems.We found that conventional RC can effectively predict time series,but it is not enough to characterize the dynamical process of the coupled system changing with the coupling strength.Therefore,we further consider the algorithm of adding parameter channels.2.We predict transitions to phase and lag synchronizatioins by parameter-aware RC algorithms.Due to the limitation of the parameter-aware RC algorithm in predicting the length of time series,we propose an improved parameter channel RC algorithm.Based on the extra channel added to the controlling parameters,we also add proper bias terms and an intermittent driving variable of the target system,which help us to realize the reliable long-term prediction of phase variables.Thus,we accurately identify the transition process of phase and lag synchronization under weak coupling strength.Besides,we also predict the asymmetric coupling direction between chaotic systems under weak coupling,which shows high potential for network link predictions.3.We propose a RC classification model to distinguish chaotic series from random counter parts.In particular,four most difficult cases of the SPROTT are successfully distinguished from each other,which has been further validated by experimental ECG data.The results show that the RC classification model can return different characteristic values.In conclusion,we propose an improved parameter-aware RC algorithm to achieve a more reliable long-term prediction of phase variables.Also,we apply the algorithm to predicting coupling direction and put forward the RC classification model.Our research provides new ideas for wide applications of RC.