Generalized attracting horseshoe in the Rössler attractor

Karthik Murthy, Ian Jordan, Parth Sojitra, Aminur Rahman, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

Abstract

We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations—realizable by a rather simple electronic circuit—capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincaré section yielding the desired map is described, but not pursued due to its complexity, which makes the construction of a circuit realization exceedingly difficult. Instead, the generalized attracting horseshoe and its trapping region is obtained by using a carefully chosen Poincaré map of the Rössler attractor. Novel numerical techniques are employed to iterate the map of the trapping region to approximate the chaotic strange attractor contained in the generalized attracting horseshoe, and an electronic circuit is constructed to produce the map. Several potential applications of the idea of a generalized attracting horseshoe and a physical electronic circuit realization are proposed.

Original languageEnglish (US)
Article number30
Pages (from-to)1-12
Number of pages12
JournalSymmetry
Volume13
Issue number1
DOIs
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Keywords

  • Electronic circuits
  • Generalized attracting horseshoe
  • Poincaré map
  • Strange attractors

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