Loading...
Please wait, while we are loading the content...
Supercritical Hopf bifurcation and Turing patterns for an activator and inhibitor model with different sources
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Jinliang Hou, Xiaojie |
| Copyright Year | 2018 |
| Abstract | We study the pattern generatingmechanism of a generalized Gierer–Meinhardt model with diffusions. We show the existence and stability of the Hopf bifurcation for the corresponding kinetic system under certain conditions. With spatial uneven diffusions, the obtained stable Hopf periodic solution may become unstable, which results in Turing instability. We derive conditions for the existence of Turing instability. Numerical simulations reveal that the Turing patterns are of stripe and spot shapes. In the analysis, we use bifurcation analysis, center manifold reduction for ordinary differential equations and partial differential equations. Though the Gierer–Meinhardt system is classical, our system with more general settings has yet to be analyzed in the literature. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-018-1697-5 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Anatomic bifurcation Bifurcation (procedure) Bifurcation theory Control theory Diffusion Hopf bifurcation Instability Kinetics Magnetic stripe card Numerical linear algebra Simulation The Chemical Basis of Morphogenesis Turing machine Unstable Medical Device Problem manifold |
| Content Type | Text |
| Resource Type | Article |
