是什么驱动了复杂系统的瞬态行为？
What drives transient behaviour in complex systems?
摘要：
我们研究由一组非线性常微分方程描述的复杂系统的动力学中的瞬态行为。讨论了瞬态轨迹的失稳性质及其与基于特征值的线性化过程的关系。该复杂性被实现为从修改的May-Wigner模型中提取的随机矩阵。基于系统的初始响应，我们确定了一个新的稳定瞬态制度。我们计算的典型和极端的瞬态轨迹发现高斯分布和Tracy-Widom分布在极值统计的确切丰度。我们确定的自由度驱动瞬态行为连接到本征向量和编码的非正交矩阵$T_0$。因此，我们扩展的May-Wigner模型包含一个阶段与典型的瞬态轨迹存在。在消失的$T_0$限制，它描述了一个正常的矩阵的轨迹的确切的规范。
英文摘要：
We study transient behaviour in the dynamics of complex systems described by a set of non-linear ODE's. Destabilizing nature of transient trajectories is discussed and its connection with the eigenvalue-based linearization procedure. The complexity is realized as a random matrix drawn from a modified May-Wigner model. Based on the initial response of the system, we identify a novel stable-transient regime. We calculate exact abundances of typical and extreme transient trajectories finding both Gaussian and Tracy-Widom distributions known in extreme value statistics. We identify degrees of freedom driving transient behaviour as connected to the eigenvectors and encoded in a non-orthogonality matrix $T_0$. We accordingly extend the May-Wigner model to contain a phase with typical transient trajectories present. An exact norm of the trajectory is obtained in the vanishing $T_0$ limit where it describes a normal matrix.
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