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Detecting Folds in Chaotic Processes By Mapping the Convex Hull

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Dynamics of Complex Interconnected Biological Systems

Part of the book series: Mathematical Modelling ((MMO,volume 6))

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Abstract

An approximate tesselation map is used to detect global foldings in reconstructed time series by mapping the boundary of the convex hull of the reconstruction. This technique is applied to the Hénon map and the Lynx population data and in the latter case shows that a model of the system requires more than two degrees of freedom.

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References

  1. Takens F., Detecting Strange Attractor in Turbulence., Dynamical Systems and Turbulence. Lecture Notes in Mathematics. Vol. 898, (1980), Rand D.A. and Young L.S., eds, pp. 365–381. Springer-Verlag, New York.

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  6. Cambell M.J., and Walker, A.M., A Survey of Statistical Work on the Mackenzie River Series of Annual Canadian Lynx Trappings for the Years 1821–1934 and a New Analysis,1977, J. Roy. Stat. Soc A, 140, part 4, pp. 411–431.

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© 1990 Birkhäuser Boston

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Glover, J.N. (1990). Detecting Folds in Chaotic Processes By Mapping the Convex Hull. In: Vincent, T.L., Mees, A.I., Jennings, L.S. (eds) Dynamics of Complex Interconnected Biological Systems. Mathematical Modelling, vol 6. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6784-0_7

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  • DOI: https://doi.org/10.1007/978-1-4684-6784-0_7

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6786-4

  • Online ISBN: 978-1-4684-6784-0

  • eBook Packages: Springer Book Archive

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