PMID: 11909235Mar 23, 2002Paper

Bifurcations of synchronized responses in synaptically coupled Bonhöffer-van der Pol neurons

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kunichika TsumotoHiroshi Kawakami

Abstract

The Bonhöffer-van der Pol (BvdP) equation is considered as an important model for studying dynamics in a single neuron. In this paper, we investigate bifurcations of periodic solutions in model equations of four and five BvdP neurons coupled through the characteristics of synaptic transmissions with a time delay. The model can be considered as a dynamical system whose solution includes jumps depending on a condition related to the behavior of the trajectory. Although the solution is discontinuous, we can define the Poincaré map as a synthesis of successive submaps, and give its derivatives for obtaining periodic points and their bifurcations. Using our proposed numerical method, we clarify mechanisms of bifurcations among synchronized oscillations with phase-locking patterns by analyzing periodic solutions observed in the coupling system and its subsystems. Moreover, we show that a global behavior of chaotic itinerancy or a phenomenon of chaotic transitions among several quasiattracting states can be observed in higher-dimensional systems of the synaptically four and five coupled neurons.

References

Mar 15, 1992·Physical Review. a·D GolombH Sompolinsky
Nov 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D HanselC Meunier

❮ Previous
Next ❯

Citations

Aug 11, 2007·Neural Networks : the Official Journal of the International Neural Network Society·Takashi Kanamaru
Mar 12, 2019·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Yasuo Kuniyoshi
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexey K KryukovJürgen Kurths
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Slaven Peles, Kurt Wiesenfeld

❮ 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
D V SenthilkumarJürgen Kurths
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Dan Stahlke, Renate Wackerbauer
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
T Kanamaru, Y Okabe
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Renate Wackerbauer
© 2022 Meta ULC. All rights reserved