Periodically kicked hard oscillators

Chaos
G. A. CecchiA. J. Santillan

Abstract

A model of a hard oscillator with analytic solution is presented. Its behavior under periodic kicking, for which a closed form stroboscopic map can be obtained, is studied. It is shown that the general structure of such an oscillator includes four distinct regions; the outer two regions correspond to very small or very large amplitude of the external force and match the corresponding regions in soft oscillators (invertible degree one and degree zero circle maps, respectively). There are two new regions for intermediate amplitude of the forcing. Region 3 corresponds to moderate high forcing, and is intrinsic to hard oscillators; it is characterized by discontinuous circle maps with a flat segment. Region 2 (low moderate forcing) has a certain resemblance to a similar region in soft oscillators (noninvertible degree one circle maps); however, the limit set of the dynamics in this region is not a circle, but a branched manifold, obtained as the tangent union of a circle and an interval; the topological structure of this object is generated by the finite size of the repelling set, and is therefore also intrinsic to hard oscillators.

References

Jul 15, 1977·Science·M C Mackey, L Glass
Feb 1, 1990·International Journal of Cardiology·Q Tong, Z Liu
Feb 1, 1990·Theoretical Population Biology·Z B Zeng, C C Cockerham
Jan 1, 1984·Journal of Mathematical Biology·J P Keener, L Glass
Mar 15, 1987·Physical Review A: General Physics·E J Ding

❮ Previous
Next ❯

Citations

Dec 1, 1995·Chaos·Gustavo StolovitzkyLawrence Sirovich
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Chacón, A Martínez García-Hoz
Sep 16, 2000·Physical Review Letters·V M EguíluzM O Magnasco
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H CroisierP C Dauby

❮ 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
R Chacón, A Martínez García-Hoz
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
R Chacón, A Martínez García-Hoz
© 2022 Meta ULC. All rights reserved