Complicated Dynamics Of Reservoir Computing System Based On Delayed Photoelectric Feedback

Reservoir Computation(RC)is a new technology that uses nonlinear dynamical system as reservoir to realize information processing.It originated from the recurrent neural network(RNNs).By improving the training algorithm,it avoids the disadvantage of training difficulties of recurrent neural network,and has the advantages of fast processing speed,large computing capacity,and simple physical implementation.Generally,the richer the reservoir dynamics,the better the system performance,the stronger the nonlinear approximation ability,and the higher the accuracy.In order to achieve the excellent performance of the system,it is very significant to study the influence of system parameters on its dynamic behavior.Supported by the National Natural Science Foundation of China(Nos.11972327 and 11372282),we consider the complicated dynamics of two RC systems based on optoelectronic feedback in this dissertation.These two systems are more classical in the photonic RC and have a wide range of uses.The study is conducive to the rational selection of parameters in solving problems and enriching the dynamics of the reservoir.Since the dynamics of the systems near the double Hopf bifurcation point are relatively rich,so we mainly study the double Hopf bifurcation behaviors of these two systems.Firstly,we give the sufficient conditions and necessary conditions for the occurrence of local double Hopf bifurcations.Secondly,we use DDE-BIFTOOL to draw Hopf bifurcation critical curves,and their intersection points may be double Hopf bifurcation points.Then we draw the eigenvalue distribution of these intersection points to find the points that satisfy the conditions for the occurrence of local double Hopf bifurcations.Then,we employ the method of multiple scales(MMS)to obtain their normal forms of the local double Hopf bifurcation near the double Hopf bifurcation points.By analyzing normal forms,we get unfolding and classifications near the double Hopf bifurcation points.Finally,the numerical simulation software Win PP is used to verify the analysis results.For the first RC based on photoelectric feedback Semiconductor laser(SL),we find the dynamic phenomena such as stable equilibrium,periodic and quasi-periodic solutions.For the second deep RC based on photoelectric feedback,we find bistability,chaos and other complicated dynamics.These results can provide a theoretical basis for researchers to choose system parameters to solve practical problems.The features and innovations of this dissertation are as follows:1.We study the double Hopf bifurcation behaviors of the reservoir computing system based on the delay optoelectronic feedback SL and the deep reservoir computing system based on delay optoelectronic feedback using the method of multiple scales,and four types of double Hopf bifurcations are found,showing that the rich dynamics of the delay reservoir computing systems;2.In the deep reservoir computing system based on delay optoelectronic feedback,we found Bistability and two chaos routes: Periodic Doubling to Chaos and Period 1 to Chaos.Compared with the single layer reservoir computing system,the deep reservoir computing system has more complex dynamics,which may be the advantage of the deep reservoir computing system.