Numerical bifurcation analysis of a 3D turing-type reaction-diffusion model

作者：Song Weiyan^*; Wubs Fred; Thies Jonas; Baars Sven

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 60: 145-164.

DOI：10.1016/j.cnsns.2018.01.003

• Continuation
• Pattern formation
• Bifurcation diagram
• Stability

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 eigen-value 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.

• 出版日期2018-7