Numerical bifurcation analysis of a 3D Turing-type reaction-diffusion model. (English) Zbl 1470.65183

Summary: We perform a numerical study of a two-component reaction-diffusion model. By using numerical continuation methods, combined with state-of-the-art sparse linear and eigenvalue solvers, we systematically compute steady state solutions and analyze their stability and relations in both two and three space dimensions. The approach gives a more reliable and complete picture than previous efforts based on time integration schemes and is also typically much more efficient in terms of computing time. We are therefore able to produce a rich bifurcation diagram showing a variety of solution patterns and transitions.


65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35K40 Second-order parabolic systems
35K57 Reaction-diffusion equations


JDQZ; Trilinos; ML; JDQR
Full Text: DOI


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