Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction

Abstract

[eng] It is shown that the nonlinear dynamics of chaotic time-delay systems can be reconstructed</p><p>using a new type of neural network with two modules: one for nonfeedback part with input</p><p>data delayed by the embedding time, and a second one for the feedback part with input data</p><p>delayed by the feedback time. The method is applied to both simulated and experimental data</p><p>from an electronic analog circuit of the Mackey–Glass system. Better results are obtained for</p><p>the modular than for feedforward neural networks for the same number of parameters. It is</p><p>found that the complexity of the neural network model required to reconstruct nonlinear</p><p>dynamics does not increase with the delay time. Synchronization between the data and the</p><p>model with diffusive coupling is also achieved. We have also shown by iterating the model</p><p>from the present point that the dynamics can be predicted with a forecast horizon larger than</p><p>the feedback delay time.</p>