Sequence of Routes to Chaos in a Lorenz-Type System

Fangyan Yang, Yongming Cao, Lijuan Chen and Qingdu Li

Discrete Dynamics in Nature and Society, 2020, vol. 2020, 1-10

Abstract:

This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos ( ) and a sequence of sub-bifurcation routes with isolated sub-branches to chaos. When is odd, the isolated sub-branches are from a period- limit cycle, followed by twin period- limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When is even, the isolated sub-branches are from twin period- limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2020/3162170.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2020/3162170.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:3162170

DOI: 10.1155/2020/3162170

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().