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Accurate approximation of homoclinic solutions in Gray–Scott kinetic model

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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.
Keywords
MatCont, Bogdanov–Takens bifurcation, homoclinic orbit, STIRRED TANK REACTOR, AUTOCATALYTIC REACTIONS, BIFURCATION-ANALYSIS, OSCILLATIONS, MATCONT, FORMS, Gray–Scott model

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Chicago
Kuznetsov, Yuri A, Hil GE Meijer, Bashir Al-Hdaibat, and Willy Govaerts. 2015. “Accurate Approximation of Homoclinic Solutions in Gray–Scott Kinetic Model.” International Journal of Bifurcation and Chaos 25 (9).
APA
Kuznetsov, Yuri A, Meijer, H. G., Al-Hdaibat, B., & Govaerts, W. (2015). Accurate approximation of homoclinic solutions in Gray–Scott kinetic model. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 25(9).
Vancouver
1.
Kuznetsov YA, Meijer HG, Al-Hdaibat B, Govaerts W. Accurate approximation of homoclinic solutions in Gray–Scott kinetic model. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2015;25(9).
MLA
Kuznetsov, Yuri A, Hil GE Meijer, Bashir Al-Hdaibat, et al. “Accurate Approximation of Homoclinic Solutions in Gray–Scott Kinetic Model.” INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 25.9 (2015): n. pag. Print.
@article{6922082,
  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.},
  articleno    = {1550125},
  author       = {Kuznetsov, Yuri A and Meijer, Hil GE and Al-Hdaibat, Bashir and Govaerts, Willy},
  issn         = {0218-1274},
  journal      = {INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS},
  keyword      = {MatCont,Bogdanov--Takens bifurcation,homoclinic orbit,STIRRED TANK REACTOR,AUTOCATALYTIC REACTIONS,BIFURCATION-ANALYSIS,OSCILLATIONS,MATCONT,FORMS,Gray--Scott model},
  language     = {eng},
  number       = {9},
  pages        = {10},
  title        = {Accurate approximation of homoclinic solutions in Gray--Scott kinetic model},
  url          = {http://dx.doi.org/10.1142/S0218127415501254},
  volume       = {25},
  year         = {2015},
}

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