Gurevich S V, Amiranashvili Sh, Purwins H-G
Institut für Angewandte Physik, Corrensstr. 2/4, D-48149 Münster, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Dec;74(6 Pt 2):066201. doi: 10.1103/PhysRevE.74.066201. Epub 2006 Dec 1.
We investigate the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. A change of the time constants of the inhibitors can lead to a destabilization of the stationary solution. The special case we are interested in is that the breathing mode becomes unstable first and the stationary dissipative soliton undergoes a bifurcation from a stationary to a "breathing" state. This situation is analyzed performing a two-time-scale expansion in the vicinity of the bifurcation point thereby obtaining the corresponding amplitude equation. Also numerical simulations are carried out showing good agreement with the analytical predictions.
我们研究了一个具有一个激活剂和两个抑制剂的三分量反应扩散系统的局域定态解的稳定性。抑制剂时间常数的变化会导致定态解失稳。我们感兴趣的特殊情况是，呼吸模式首先变得不稳定，定态耗散孤子经历从定态到“呼吸”态的分岔。通过在分岔点附近进行双时间尺度展开来分析这种情况，从而得到相应的振幅方程。还进行了数值模拟，结果与解析预测吻合良好。
