par Kaufman, Marcelle 
Référence The Bulletin of Mathematical Biophysics, 37, 6, page (589-636)
Publication Publié, 1975-12
Référence The Bulletin of Mathematical Biophysics, 37, 6, page (589-636)
Publication Publié, 1975-12
Article révisé par les pairs
| Résumé : | The steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network. A detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions. The characteristics of the dissipative structures are discussed and it is shown that the observed behavior depends strongly on both the boundary and initial conditions. The theoretical expressions are limited to the neighborhood of the marginal stability point. Computer simulations allow not only the verification of their predictions but also the investigation of the behavior of the system for larger deviations from the instability point. It is shown that new features such as multiplicity of solutions and secondary bifurcations can appear in this region. © 1975 Society for Mathematical Biology. |
