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Stability and Hopf Bifurcation Analysis of a Reduced Gierer–Meinhardt Model.
- Source :
-
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering . Aug2021, Vol. 31 Issue 10, p1-21. 21p. - Publication Year :
- 2021
-
Abstract
- In this paper, we consider a reduction of the Gierer–Meinhardt Activator–Inhibitor model. In the absence of diffusion, we determine the global dynamics of the homogeneous system. Then, we study the effect of the diffusion constants on the stability of a homogeneous steady state. By choosing a proper bifurcation parameter, we prove that, under some suitable conditions on the parameters, a generalized Hopf bifurcation occurs in the inhomogeneos model. We compute the normal form of this bifurcation up to the fifth order. Furthermore, the direction of the Hopf bifurcation is obtained by the normal form theory. Finally, we provide some numerical simulations to justify our theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 31
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 151880150
- Full Text :
- https://doi.org/10.1142/S0218127421501492