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Relation between observability and differential embeddings for nonlinear dynamics.
In the analysis of a scalar time series, which lies on an m-dimensional object, a great number of techniques will start by embedding such a time series in a d-dimensional space, with d>m. ThereforeExpand
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The Symmetry of Chaos
Why have scientists, engineers, and mathematicians become intrigued by chaos? Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - aExpand
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Analysis of the dynamics of a realistic ecological model
Abstract A fairly realistic three-species food chain model based on the Leslie–Gower scheme is investigated by using tools borrowed from the nonlinear dynamical systems theory. It is observed thatExpand
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Estimating the Shannon entropy: recurrence plots versus symbolic dynamics.
  • C. Letellier
  • Mathematics, Medicine
  • Physical review letters
  • 29 June 2006
Recurrence plots were first introduced to quantify the recurrence properties of chaotic dynamics. A few years later, the recurrence quantification analysis was introduced to transform graphicalExpand
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Modeling Nonlinear Dynamics and Chaos: A Review
This paper reviews the major developments of modeling techniques applied to nonlinear dynamics and chaos. Expand
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Covering dynamical systems: twofold covers.
  • C. Letellier, R. Gilmore
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and…
  • 19 December 2000
We study the relation between a dynamical system, which is unchanged (equivariant) under a discrete symmetry group G and another locally identical dynamical system with no residual symmetry. We alsoExpand
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Van der Pol and the history of relaxation oscillations: toward the emergence of a concept.
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe theExpand
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Ansatz library for global modeling with a structure selection.
The information contained in a scalar time series and its time derivatives is used to obtain a global model for the underlying dynamics. This model provides a description of the time evolution of theExpand
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How the choice of the observable may influence the analysis of nonlinear dynamical systems
Abstract A great number of techniques developed for studying nonlinear dynamical systems start with the embedding, in a d -dimensional space, of a scalar time series, lying on an m -dimensionalExpand
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Evidence for low dimensional chaos in sunspot cycles
Sunspot cycles are widely used for investigating solar activity. In 1953 Bracewell argued that it is sometimes desirable to introduce the inversion of the magnetic field polarity, and that can beExpand
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