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.
|Number of pages||10|
|Journal||International journal of bifurcation and chaos in applied sciences and engineering|
|Publication status||Published - Aug 2015|
- Bogdanov–Takens bifurcation
- Homoclinic orbit
- Gray–Scott model
Kouznetsov, I. A., Meijer, H. G. E., Al Hdaibat, B., & Govaerts, W. (2015). Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model. International journal of bifurcation and chaos in applied sciences and engineering, 25(9), 1550125. https://doi.org/10.1142/S0218127415501254