This article is devoted to the analysis of the dynamics of a complex network of unstable reaction–diffusion systems. We demonstrate the existence of a non-empty parameter regime for which synchronization occurs in non-trivial attractors. We establish a lower bound of the dimension of the global attractor in an innovative manner, by proving a novel theorem of continuity of the unstable manifold, for which we invoke a principle of spectrum perturbation of non-bounded operators. Finally, we exhibit a co-dimension 2 bifurcation of the unstable manifold which shows that synchronization is compatible with instabilities.

中文翻译：

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不稳定反应扩散系统网络的分叉与同步

本文致力于分析不稳定的反应扩散系统的复杂网络的动力学。我们证明了存在一个非空参数机制，对于它而言，在非平凡的吸引子中发生同步。通过证明不稳定流形的连续性的新定理，我们以创新的方式确定了全局吸引子维数的下界，为此我们引用了无界算子的频谱扰动原理。最后，我们展示了不稳定歧管的一个维数2分叉，这表明同步与不稳定性兼容。