Chaos-hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators

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Chaos-hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators. / Stankevich, N.; Volkov, E.

In: Chaos, Vol. 31, No. 10, 103112, 01.10.2021.

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

BibTeX

@article{88165168dbe54d5d91e7bb620e1ed5d1,

title = "Chaos-hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators",

abstract = "We investigate the dynamics of three identical three-dimensional ring synthetic genetic oscillators (repressilators) located in different cells and indirectly globally coupled by quorum sensing whereby it is meant that a mechanism in which special signal molecules are produced that, after the fast diffusion mixing and partial dilution in the environment, activate the expression of a target gene, which is different from the gene responsible for their production. Even at low coupling strengths, quorum sensing stimulates the formation of a stable limit cycle, known in the literature as a rotating wave (all variables have identical waveforms shifted by one third of the period), which, at higher coupling strengths, converts to complex tori. Further torus evolution is traced up to its destruction to chaos and the appearance of hyperchaos. We hypothesize that hyperchaos is the result of merging the saddle-focus periodic orbit (or limit cycle) corresponding to the rotating wave regime with chaos and present considerations in favor of this conclusion.",

keywords = "RELAXATION-OSCILLATORS, MULTISTABILITY, BIFURCATIONS, ATTRACTORS, MODEL",

author = "N. Stankevich and E. Volkov",

note = "Publisher Copyright: {\textcopyright} 2021 Author(s).",

year = "2021",

month = oct,

day = "1",

doi = "10.1063/5.0056907",

language = "English",

volume = "31",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics",

number = "10",

}

RIS

TY - JOUR

T1 - Chaos-hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators

AU - Stankevich, N.

AU - Volkov, E.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We investigate the dynamics of three identical three-dimensional ring synthetic genetic oscillators (repressilators) located in different cells and indirectly globally coupled by quorum sensing whereby it is meant that a mechanism in which special signal molecules are produced that, after the fast diffusion mixing and partial dilution in the environment, activate the expression of a target gene, which is different from the gene responsible for their production. Even at low coupling strengths, quorum sensing stimulates the formation of a stable limit cycle, known in the literature as a rotating wave (all variables have identical waveforms shifted by one third of the period), which, at higher coupling strengths, converts to complex tori. Further torus evolution is traced up to its destruction to chaos and the appearance of hyperchaos. We hypothesize that hyperchaos is the result of merging the saddle-focus periodic orbit (or limit cycle) corresponding to the rotating wave regime with chaos and present considerations in favor of this conclusion.

AB - We investigate the dynamics of three identical three-dimensional ring synthetic genetic oscillators (repressilators) located in different cells and indirectly globally coupled by quorum sensing whereby it is meant that a mechanism in which special signal molecules are produced that, after the fast diffusion mixing and partial dilution in the environment, activate the expression of a target gene, which is different from the gene responsible for their production. Even at low coupling strengths, quorum sensing stimulates the formation of a stable limit cycle, known in the literature as a rotating wave (all variables have identical waveforms shifted by one third of the period), which, at higher coupling strengths, converts to complex tori. Further torus evolution is traced up to its destruction to chaos and the appearance of hyperchaos. We hypothesize that hyperchaos is the result of merging the saddle-focus periodic orbit (or limit cycle) corresponding to the rotating wave regime with chaos and present considerations in favor of this conclusion.

KW - RELAXATION-OSCILLATORS

KW - MULTISTABILITY

KW - BIFURCATIONS

KW - ATTRACTORS

KW - MODEL

UR - http://www.scopus.com/inward/record.url?scp=85117101926&partnerID=8YFLogxK

U2 - 10.1063/5.0056907

DO - 10.1063/5.0056907

M3 - Article

AN - SCOPUS:85117101926

VL - 31

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 10

M1 - 103112

ER -

ID: 89228889