Beijing Normal University, 519087 Zhuhai, China.
Beijing University of Posts and Telecommunications, 100876 Beijing, China.
Phys Rev Lett. 2023 Mar 3;130(9):097401. doi: 10.1103/PhysRevLett.130.097401.
Many real-world complex systems, when hitting a tipping point, undergo irreversible sudden shifts that can eventually take a great toll on humanity and the natural world, such as ecosystem collapses, disease outbreaks, etc. Previous work has adopted approximations to predict the tipping points, but due to the nature of nonlinearity, this may lead to unexpected errors in predicting real-world systems. Here we obtain the rigorous bounds of the tipping points for general nonlinear cooperative networks. Our results offer two rigorous criteria that determine the collapse and survival of such a system. These two criteria are decided by the combined effect of dynamical parameters and interaction topology.
许多真实世界的复杂系统在达到临界点时会经历不可逆转的突然转变，最终可能会对人类和自然世界造成巨大的损失，如生态系统崩溃、疾病爆发等。之前的工作采用了近似值来预测临界点，但由于非线性的性质，这可能会导致对真实系统的预测出现意外错误。在这里，我们为一般的非线性合作网络获得了临界点的严格边界。我们的结果提供了两个严格的标准，决定了这样一个系统的崩溃和生存。这两个标准是由动力学参数和相互作用拓扑的综合影响决定的。
