Geometric mechanism for antimonotonicity in scalar maps with two critical points

Silvina Ponce Dawson, Celso Grebogi, Huseyin Kocak

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Concurrent creation and destruction of periodic orbits-antimonotonicity-for one-parameter scalar maps with at least two critical points are investigated. It is observed that if, for a parameter value, two critical points lie in an interval that is a chaotic attractor, then, generically, as the parameter is varied through any neighborhood of such a value, periodic orbits should be created and destroyed infinitely often. A general mechanism for this complicated dynamics for one-dimensional multimodal maps is proposed similar to the one of contact-making and contact-breaking homoclinic tangencies in two-dimensional dissipative maps. This subtle phenomenon is demonstrated in a detailed numerical study of a specific one-dimensional cubic map.

Original languageEnglish (US)
Pages (from-to)1676-1682
Number of pages7
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume48
Issue number3
DOIs
StatePublished - 1993

Fingerprint

Critical point
critical point
Scalar
scalars
Periodic Orbits
Contact
orbits
Homoclinic
Chaotic Attractor
destruction
Concurrent
Numerical Study
intervals
Interval

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Geometric mechanism for antimonotonicity in scalar maps with two critical points. / Dawson, Silvina Ponce; Grebogi, Celso; Kocak, Huseyin.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 48, No. 3, 1993, p. 1676-1682.

Research output: Contribution to journalArticle

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