PMID: 11909215Mar 23, 2002Paper

Self-similar organization of Gavrilov-Silnikov-Newhouse sinks

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
B K Goswami, Sourish Basu

Abstract

The numerical analyses of the Hénon map suggest the following features. As we increase the value of the control parameter around each stable period of the period-1 branch, an infinitely large series of period n-tupled saddle nodes appears in the following sequence (n= ...,5,4,3). The limit of each series is the infinitely large set of homoclinic points, created at the homoclinic tangency for the respective flip saddle (boundary saddle in the case of period 1). These observations are in good agreement with the predictions of Gavrilov, Silnikov, and Robinson. Each newly created sink, referred to as Gavrilov-Silnikov (GS) sink, later constitutes a first-order secondary cascade. The flip (boundary) saddles of these cascades also exhibit homoclinic tangency. Past such tangency, around the respective GS sink, an infinitely large series of period n-tupled saddle nodes (n= ...,5,4,3) seems to appear in a similar manner. The newly created GS sinks later constitute second-order secondary cascades. These phenomena, comprised of the homoclinic tangency of a flip (boundary) saddle, followed by the sequential appearance of an infinitely large sequence of period n-tupled saddle nodes around the respective GS sink, appear to recur in a self-si...Continue Reading

References

Jul 15, 1987·Physical Review A: General Physics·B K Goswami, D J Biswas
Mar 1, 1989·Physical Review A: General Physics·E EschenaziR Gilmore
Jun 15, 1991·Physical Review. a·C ScheffczykW Lauterborn
Dec 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G B MindlinR Gilmore
Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·R Gilmore, J W McCallum
Jul 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·U FeudelJ A Yorke
Oct 4, 2000·Physical Review Letters·A N Pisarchik, B K Goswami
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B K Goswami

❮ Previous
Next ❯

Citations

Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Binoy Krishna Goswami, Sourish Basu
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B K Goswami
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B K GoswamiF T Arecchi
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B K Goswami

❮ 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 Letters
A de LozarB Hof
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Lina Kim, Jeff Moehlis
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
J HeraultP-Y Longaretti
Chaos
Tobias M Schneider, Bruno Eckhardt
© 2022 Meta ULC. All rights reserved