The application of symplectic geometry on nonlinear dynamics analysis of the experimental data
2002 14th International Conference on Digital Signal Processing Proceedings. DSP 2002 (Cat. No.02TH8628) - Tập 2 - Trang 1137-1140 vol.2
Tóm tắt
For nonlinear dynamic analysis of the experiment data, one often uses SVD decomposition to reconstruct embedding dimension of attractor because of its simpleness. However, it is hardly for singular value decomposition (SVD) decomposition to get good results in the attractor reconstruction of the experiment data. For this, symplectic geometry method is proposed to estimate embedding dimension of reconstruction attractor in this paper. We illustrate the feasibility of this method and give the embedding dimension of the action surface EMG signal.
Từ khóa
#Geometry #Nonlinear dynamical systems #Delay effects #Electromyography #Surface reconstruction #Chaos #State-space methods #Time series analysis #Data analysis #MechatronicsTài liệu tham khảo
10.1016/0167-2789(92)90085-2
10.1109/18.32121
10.1016/0375-9601(89)90169-2
10.1103/PhysRevA.36.340
10.1016/0167-2789(89)90263-7
10.1007/978-3-642-71001-8_18
palus, 1992, Singular-value decomposition in attractor reconstruction pitfalls and precautions Physica D, 55, 221
feng, 1985, Proceeding of the 5-th Intern Symposium on Differential Geometry& Differential Equations Beijing 1984, 42
mackay, 1998, Stability of discrete breathers Physica D, 119, 148
10.1016/S0020-7462(99)00062-1
10.1016/S0167-2789(98)00168-7
gong, 1998, Determining the degree of chaos from analysis of ISI time series in nervous system: a comparison between correlation dimension and nonlinear forecasting methods, Bio Cybernet, 78, 159, 10.1007/s004220050422
10.1016/0167-2789(93)90009-P
10.1073/pnas.88.6.2297
10.1103/PhysRevLett.45.712
takens, 1980, Detecting Strange Attractors in Turbulence. In: Dynamical Systems and Turbulence, Lecrure Notes in Mathematics, 898, 366, 10.1007/BFb0091924
cheng, 1994, Orthoggonal Projection, Embedding Dimension and Sample size in chaotic times series from a statistical perspective, Nonlinear Time Series and Chaos, 2, 1
10.1142/S0218127496000230
10.1016/0167-2789(86)90031-X
10.1016/S0960-0779(00)00225-3
10.1016/S0375-9601(01)00668-5
10.1016/0024-3795(84)90034-X