Universal geometry in the parameter plane of dissipative dynamical systems

J. Ringland; M. Schell

doi:10.1209/0295-5075/12/7/004

Universal geometry in the parameter plane of dissipative dynamical systems

J. Ringland
, M. Schell

Mathematics

Southern Methodist University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A new kind of quantitative universality in dissipative nonlinear dynamical systems is presented: A universality of shape of the regions in the parameter plane where a periodic orbit is stable. It arises in the two-extremum one-dimensional map, a model prototype for systems where two folding processes in the phase space interact. Two numerical examples of the realization of the universal geometry are given.

Original language	English
Pages (from-to)	595-601
Number of pages	7
Journal	Europhysics Letters
Volume	12
Issue number	7
DOIs	https://doi.org/10.1209/0295-5075/12/7/004
State	Published - Aug 1 1990

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abstract = "A new kind of quantitative universality in dissipative nonlinear dynamical systems is presented: A universality of shape of the regions in the parameter plane where a periodic orbit is stable. It arises in the two-extremum one-dimensional map, a model prototype for systems where two folding processes in the phase space interact. Two numerical examples of the realization of the universal geometry are given.",

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AB - A new kind of quantitative universality in dissipative nonlinear dynamical systems is presented: A universality of shape of the regions in the parameter plane where a periodic orbit is stable. It arises in the two-extremum one-dimensional map, a model prototype for systems where two folding processes in the phase space interact. Two numerical examples of the realization of the universal geometry are given.

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Universal geometry in the parameter plane of dissipative dynamical systems

Abstract

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