On the Identification and Generation of Discrete-Time Chaotic Systems with Recurrent Neural Networks

We address the identification and generation of the discrete-time chaotic system (DTCS) with a two-layered recurrent neural network (RNN). First, we propose an identification procedure of the DTCS in which the RNN is required to have less layers than in the conventional procedures. Next, based on Li–Yorke theorem, we propose a generation procedure which enables us to predict a range of chaotic behavior of the DTCS in advance. Simulation results demonstrate that the proposed identification procedure, employing the Levenberg–Marquardt algorithm and a two-layered RNN, requires lower computational complexity than the conventional identification procedures at comparable performance.