TY - JOUR
T1 - Predicting amplitude death with machine learning
AU - Xiao, Rui
AU - Kong, Ling Wei
AU - Sun, Zhong Kui
AU - Lai, Ying Cheng
N1 - Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/7
Y1 - 2021/7
N2 - In nonlinear dynamics, a parameter drift can lead to a sudden and complete cessation of the oscillations of the state variables - the phenomenon of amplitude death. The underlying bifurcation is one at which the system settles into a steady state from chaotic or regular oscillations. As the normal functioning of many physical, biological, and physiological systems hinges on oscillations, amplitude death is undesired. To predict amplitude death in advance of its occurrence based solely on oscillatory time series collected while the system still functions normally is a challenge problem. We exploit machine learning to meet this challenge. In particular, we develop the scheme of "parameter-aware"reservoir computing, where training is conducted for a small number of bifurcation parameter values in the oscillatory regime to enable prediction upon a parameter drift into the regime of amplitude death. We demonstrate successful prediction of amplitude death for three prototypical dynamical systems in which the transition to death is preceded by either chaotic or regular oscillations. Because of the completely data-driven nature of the prediction framework, potential applications to real-world systems can be anticipated.
AB - In nonlinear dynamics, a parameter drift can lead to a sudden and complete cessation of the oscillations of the state variables - the phenomenon of amplitude death. The underlying bifurcation is one at which the system settles into a steady state from chaotic or regular oscillations. As the normal functioning of many physical, biological, and physiological systems hinges on oscillations, amplitude death is undesired. To predict amplitude death in advance of its occurrence based solely on oscillatory time series collected while the system still functions normally is a challenge problem. We exploit machine learning to meet this challenge. In particular, we develop the scheme of "parameter-aware"reservoir computing, where training is conducted for a small number of bifurcation parameter values in the oscillatory regime to enable prediction upon a parameter drift into the regime of amplitude death. We demonstrate successful prediction of amplitude death for three prototypical dynamical systems in which the transition to death is preceded by either chaotic or regular oscillations. Because of the completely data-driven nature of the prediction framework, potential applications to real-world systems can be anticipated.
UR - http://www.scopus.com/inward/record.url?scp=85110353249&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.104.014205
DO - 10.1103/PhysRevE.104.014205
M3 - 文章
C2 - 34412238
AN - SCOPUS:85110353249
SN - 1539-3755
VL - 104
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 1
M1 - 014205
ER -