Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

Iouri Aleksandrovitsj Kouznetsov; Hil Gaétan Ellart Meijer; B. Al Hdaibat; W. Govaerts

doi:10.1142/S0218127415501254

Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

Iouri Aleksandrovitsj Kouznetsov, Hil Gaétan Ellart Meijer, B. Al Hdaibat, W. Govaerts

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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 language	English
Pages (from-to)	1550125
Number of pages	10
Journal	International journal of bifurcation and chaos in applied sciences and engineering
Volume	25
Issue number	9
DOIs	https://doi.org/10.1142/S0218127415501254
Publication status	Published - Aug 2015

Keywords

2023 OA procedure
Bogdanov–Takens bifurcation
MatCont
Homoclinic orbit
Gray–Scott model

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10.1142/S0218127415501254

S0218127415501254Final published version, 338 KBLicence: Taverne

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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 = "2023 OA procedure, Bogdanov–Takens bifurcation, MatCont, Homoclinic orbit, Gray–Scott model",

author = "Kouznetsov, {Iouri Aleksandrovitsj} and Meijer, {Hil Ga{\'e}tan Ellart} and {Al Hdaibat}, B. and W. Govaerts",

year = "2015",

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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.

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 - 2023 OA procedure

KW - Bogdanov–Takens bifurcation

KW - MatCont

KW - Homoclinic orbit

KW - Gray–Scott model

U2 - 10.1142/S0218127415501254

DO - 10.1142/S0218127415501254

M3 - Article

SN - 0218-1274

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

IS - 9

ER -

Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model

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