Journal ArticleDOI
Phase space reconstruction for symmetric dynamical systems
Gregory P. King,Ian Stewart +1 more
TLDR
In this paper, the Packard-Takens approach was extended to a single equivariant observation, taking values not in the real numbers R but in a linear representation V of the symmetry group G.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1992-09-15. It has received 35 citations till now. The article focuses on the topics: Attractor & Equivariant map.read more
Citations
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Journal ArticleDOI
Hexapodal gaits and coupled nonlinear oscillator models
James J. Collins,Ian Stewart +1 more
TL;DR: The present analysis leads to a natural classification of hexapodal gaits by symmetry and to natural sequences of gait bifurcations, which relates observed gaits to the overall organizational structure of the underlying CPG.
Journal ArticleDOI
On the non-equivalence of observables in phase-space reconstructions from recorded time series
TL;DR: In this paper, it is argued that different dynamical variables do not provide the same level of information (observability) of the underlying dynamics and, as a consequence, the quality of a global reconstruction critically depends on the recorded variable.
Journal ArticleDOI
Landslide displacement prediction using discrete wavelet transform and extreme learning machine based on chaos theory
TL;DR: The comparison results show that the chaos theory-based discrete wavelet transform (DWT)–extreme learning machine (ELM) model achieves higher prediction accuracy than do the chaotic DWT-SVM, chaoticDWT-BPNN and the single chaotic ELM models.
Posted Content
Geometrical approach to modeling of nonlinear systems from experimental data.
TL;DR: This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data and development of the proposed approach : identification of groups symmetries on the phase portraits of dynamical Systems and the method of constructing neural network predictive models.
Journal ArticleDOI
Prediction of groundwater levels using evidence of chaos and support vector machine
TL;DR: The chaotic PSO-SVM model is applied to predict the daily groundwater levels in Huayuan landslide and the weekly, monthly groundwater level in Baijiabao landslide in the Three Gorges Reservoir Area in China and shows that there are chaos characteristics in the groundwater levels.
References
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Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Journal ArticleDOI
Geometry from a Time Series
TL;DR: In this paper, the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow was determined experimentally by reconstructing phase-space pictures from the observation of a single coordinate of any dissipative dynamical system and determining the dimensionality of the system's attractor.
BookDOI
Singularities and groups in bifurcation theory
TL;DR: Singularities and groups in bifurcation theory as mentioned in this paper have been used to solve the problem of finding a group of singularities in a set of problems with multiple solutions.