Deep learning prediction of amplitude death

Abstract

Affected by parameter drift and coupling organization, nonlinear dynamical systems exhibit suppressed oscillations. This phenomenon is called amplitude death. In various complex systems, amplitude death is a typical critical phenomenon, which may lead to the functional collapse of the system. Therefore, an important issue is how to effectively predict critical phenomena based on the data in the system oscillation state. This paper proposes an enhanced Informer model to predict amplitude death. The model employs an attention mechanism to capture the long-range associations of the system time series and tracks the effect of parameter drift on the system dynamics through an accompanying parameter input channel. The experimental results based on the coupled Rössler and Lorentz systems show that the enhanced informer has higher prediction accuracy and longer effective prediction distance than the original algorithm and can predict the amplitude death of a system.

Keywords

Complex system / Amplitude death / Bifurcation parameter / Attention mechanism

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Funding

National Natural Science Foundation of China(62088101); Shanghai Municipal Science and Technology, China Major Project(2021SHZDZX0100); Shanghai Municipal Commission of Science and Technology, China(19511132101)