Neural spike renormalization. Part II - Multiversal chaos

Bo Deng

doi:10.1016/j.jde.2010.10.004

Neural spike renormalization. Part II - Multiversal chaos

Bo Deng

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

Original language	English (US)
Pages (from-to)	2958-2968
Number of pages	11
Journal	Journal of Differential Equations
Volume	250
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2010.10.004
State	Published - Mar 15 2011

Keywords

Chaotic dynamical systems
Conjugate embedding
Dense orbit
Periodic orbit
Sensitive dependence on initial conditions
Spike renormalization operator

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2010.10.004

Cite this

@article{81c44f53880a4dd185ad8f747ed8ddec,

title = "Neural spike renormalization. Part II - Multiversal chaos",

abstract = "Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.",

keywords = "Chaotic dynamical systems, Conjugate embedding, Dense orbit, Periodic orbit, Sensitive dependence on initial conditions, Spike renormalization operator",

author = "Bo Deng",

year = "2011",

month = mar,

day = "15",

doi = "10.1016/j.jde.2010.10.004",

language = "English (US)",

volume = "250",

pages = "2958--2968",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "6",

}

TY - JOUR

T1 - Neural spike renormalization. Part II - Multiversal chaos

AU - Deng, Bo

PY - 2011/3/15

Y1 - 2011/3/15

N2 - Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

AB - Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

KW - Chaotic dynamical systems

KW - Conjugate embedding

KW - Dense orbit

KW - Periodic orbit

KW - Sensitive dependence on initial conditions

KW - Spike renormalization operator

UR - http://www.scopus.com/inward/record.url?scp=79551618757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551618757&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2010.10.004

DO - 10.1016/j.jde.2010.10.004

M3 - Article

AN - SCOPUS:79551618757

SN - 0022-0396

VL - 250

SP - 2958

EP - 2968

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

Neural spike renormalization. Part II - Multiversal chaos

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this