Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)
1 Downloads (Pure)

Abstract

The second-order predictor for the homoclinic orbit is applied to the Gray–Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov–Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov–Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.
Original languageUndefined
Pages (from-to)1550125
Number of pages10
JournalInternational journal of bifurcation and chaos in applied sciences and engineering
Volume25
Issue number9
DOIs
Publication statusPublished - Aug 2015

Keywords

  • EWI-26246
  • Bogdanov–Takens bifurcation
  • MatCont
  • IR-97114
  • Homoclinic orbit
  • METIS-312705
  • Gray–Scott model

Cite this

@article{70909173e4004ac283e97fa6e691cccf,
title = "Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model",
abstract = "The second-order predictor for the homoclinic orbit is applied to the Gray–Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov–Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov–Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.",
keywords = "EWI-26246, Bogdanov–Takens bifurcation, MatCont, IR-97114, Homoclinic orbit, METIS-312705, Gray–Scott model",
author = "Kouznetsov, {Iouri Aleksandrovitsj} and Meijer, {Hil Ga{\'e}tan Ellart} and {Al Hdaibat}, B. and W. Govaerts",
note = "eemcs-eprint-26246",
year = "2015",
month = "8",
doi = "10.1142/S0218127415501254",
language = "Undefined",
volume = "25",
pages = "1550125",
journal = "International journal of bifurcation and chaos in applied sciences and engineering",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "9",

}

Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model. / Kouznetsov, Iouri Aleksandrovitsj; Meijer, Hil Gaétan Ellart; Al Hdaibat, B.; Govaerts, W.

In: International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25, No. 9, 08.2015, p. 1550125.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

AU - Kouznetsov, Iouri Aleksandrovitsj

AU - Meijer, Hil Gaétan Ellart

AU - Al Hdaibat, B.

AU - Govaerts, W.

N1 - eemcs-eprint-26246

PY - 2015/8

Y1 - 2015/8

N2 - The second-order predictor for the homoclinic orbit is applied to the Gray–Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov–Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov–Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.

AB - The second-order predictor for the homoclinic orbit is applied to the Gray–Scott model. The problem is used to illustrate the approximation of the homoclinic orbits near a generic Bogdanov–Takens bifurcation in n-dimensional systems of differential equations. In the process, we show that it is necessary to take (usually ignored) cubic terms in the Bogdanov–Takens normal form into account to derive a correct second-order prediction for the homoclinic bifurcation curve. The analytic solutions are compared with those obtained by numerical continuation.

KW - EWI-26246

KW - Bogdanov–Takens bifurcation

KW - MatCont

KW - IR-97114

KW - Homoclinic orbit

KW - METIS-312705

KW - Gray–Scott model

U2 - 10.1142/S0218127415501254

DO - 10.1142/S0218127415501254

M3 - Article

VL - 25

SP - 1550125

JO - International journal of bifurcation and chaos in applied sciences and engineering

JF - International journal of bifurcation and chaos in applied sciences and engineering

SN - 0218-1274

IS - 9

ER -