The prediction for chaotic trajectory from the measured data of time history, without prior knowledge of underlying dynamical model, is a challenging task in the data-driven analysis, due to its sensitivity to initial conditions. In this paper, the Long Short-Term Memory Network (LSTM) with the merge layer is proposed to predict the future states of the coupled Morris-Lecar (M-L) system with the chaotic itinerancy responses. Here, the two LSTM models with single-branch and multi-branch are constructed respectively to carry out the predictions in the multivariate loading conditions. By comparison to the network model with single-branch, the multi-branch model with adding merge layer can provide a high utilization of weights to reduce training cost greatly and receive a low prediction error, which make the multi-layer LSTM promising to estimate a high-dimensional complex dynamical behavior like transient chaotic itinerancy.
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The work is supported by the National Natural Science Foundation of China under 11772243.
The network structure diagram built after adding the merge layer
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Xue, Y., Jiang, J. & Hong, L. A LSTM based prediction model for nonlinear dynamical systems with chaotic itinerancy. Int. J. Dynam. Control (2020). https://doi.org/10.1007/s40435-020-00673-4
- Nonlinear dynamical systems
- Chaotic itinerancy
- Time series prediction
- Multivariate loading conditions