PMID: 11308570Apr 20, 2001Paper

Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map: mechanisms and their characterizations

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A Venkatesan, M Lakshmanan

Abstract

A simple quasiperiodically forced one-dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors (SNAs) in a two-parameter (A-f) space. The routes include transitions to chaos via SNAs from both a one-frequency torus and a period-doubled torus. In the former case, we identify the fractalization and type-I intermittency routes. In the latter case, we point out that at least four distinct routes for the truncation of the torus-doubling bifurcation and the creation of SNAs occur in this model. In particular, the formation of SNAs through Heagy-Hammel, fractalization, and type-III intermittent mechanisms is described. In addition, it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the attractor, which tames the growth of period-doubling bifurcation, takes place, creating the SNA. The SNAs created through different mechanisms are characterized by the behavior of the Lyapunov exponents and their variance, by the estimation of the phase sensitivity exponent, and through the distribution of finite-time Lyapunov exponents.

References

May 15, 1987·Physical Review A: General Physics·F J Romeiras, E Ott
Dec 1, 1987·Physical Review A: General Physics·C GrebogiJ A Yorke
Apr 15, 1992·Physical Review. a·T ZhouA Bulsara
Feb 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Kapitaniak
Mar 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S P KuznetsovU Feudel
Jan 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y C Lai
May 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·V S AnishchenkoO Sosnovtseva
Dec 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Nishikawa, K Kaneko
Jul 30, 1990·Physical Review Letters·W L DittoE Ott
May 2, 1994·Physical Review Letters·J M FlessellesS Jucquois
Dec 16, 1996·Physical Review Letters·T Yalçinkaya, Y C Lai
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A VenkatesanR Ramaswamy
Mar 1, 1995·Chaos·Arkady S. Pikovsky, Ulrike Feudel

❮ Previous
Next ❯

Citations

Aug 4, 2007·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·M DiestelhorstD Hesse
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xingang WangChoy Heng Lai
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E J NgamgaJ Kurths
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D V SenthilkumarM Lakshmanan
Jan 8, 2020·Communications Biology·Daniel TokerMark D'Esposito
Jun 17, 2018·Physical Review. E·M Sathish AravindhM Lakshmanan
Jan 12, 2020·Communications Biology·Daniel TokerMark D'Esposito
Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K ThamilmaranM Lakshmanan
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sang-Yoon KimEdward Ott
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexey Yu Jalnine, Andrew H Osbaldestin

❮ Previous
Next ❯

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Sang-Yoon KimE Ott
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Sandip DattaAwadhesh Prasad
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M Romero-Bastida, Alan Yoshio Reyes-Martínez
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Xingang WangChoy-Heng Lai
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Jong-Won KimE Ott
© 2021 Meta ULC. All rights reserved