Global solutions for quasilinear parabolic systems with cross-diffusion effects
Nonlinear Analysis: Theory, Methods & Applications
Stability and bifurcation in a diffusive prey-predator system: non-linear bifurcation analysis
The Korean Journal of Computational & Applied Mathematics
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This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.