title: Intrinsic mode functions locate implicit turbulent attractors in time in frontal lobe MEG recordings.
abstract: In seeking evidence for the presence and characteristic range of coupled time scale(s) of putative implicit turbulent attractors of dorsal frontal lobe magnetic fields, the recorded nonstationary, nonlinear MEG signals were non-orthogonally decomposed using Huang's Empirical Mode Decomposition, EMD, (Huang and Attoh-Okine, 2005) into 16 Intrinsic Mode Functions, EMD→IMFi, i=1…16. Measures known to be invariant in non-uniformly hyperbolic (turbulent) dynamical systems, topological entropy, hT, metric entropy, hM, non-uniform entropy, hU and power spectral scaling exponent, α, were imposed on each of the IMFi which evidenced most clearly an invariant temporal scale zone of IMFi, i=6…11, for hT, which we have found to be the most robust of invariant measures of MEG's magnetic field turbulent attractors (Mandell et al., 2011a,b; Mandell, 2013). The ergodic theory of dynamical systems (Walters, 1982; Pollicott and Yuri, 1998) allows the inference that an implicit attractor with consistently hT>0 will also evidence at least one positive Lyapounov exponent indicating the presence of a turbulent attractor with exponential separation of nearby initial conditions, exponential convergence of distant points and disordering, mixing, of orbital sequences. It appears that this approach permits the inference of the presence of chaotic, turbulent attractor and its characteristic time scales without the invocation of arbitrary n-dimensional embedding, phase space reconstructions or (inappropriate) orthogonal decompositions.
authors.affiliation: Department of Computer Science and Engineering, College of Information Engineering, Shanghai Maritime University, Shanghai 201306, PR China; Department of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92093, USA.
authors.forename: X
authors.initials: X
authors.lastname: Huang
authors.affiliation: Institute of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, PR China; Department of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92093, USA.
authors.forename: L
authors.initials: L
authors.lastname: Huang
authors.affiliation: Swartz Center for Computational Neuroscience, Engineering, Institute of Engineering in Medicine, University of California at San Diego, La Jolla, CA 92093, USA.
authors.forename: T-P
authors.initials: TP
authors.lastname: Jung
authors.affiliation: Department of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92093, USA. Electronic address: ckcheng@ucsd.edu.
authors.forename: C-K
authors.initials: CK
authors.lastname: Cheng
authors.affiliation: Multi Media Imaging Laboratory, Department of Psychiatry, University of California at San Diego School of Medicine, La Jolla, CA 92093, USA; Fetzer Franklin Fund of the John Fetzer Memorial Trust, Kalamazoo, MI, USA.
authors.forename: A J
authors.initials: AJ
authors.lastname: Mandell
mesh_terms: D019277:Entropy; D005260:Female; D005625:Frontal Lobe / Q000502:physiology*; D006801:Humans; D015225:Magnetoencephalography; D008297:Male; D008954:Models, Biological; D017711:Nonlinear Dynamics; D013057:Spectrum Analysis; D013997:Time Factors
keywords: Empirical Mode Decomposition; implicit turbulent attractor; metric entropy; non-uniform entropy; power spectral scaling exponent α; topological entropy