Department of Computational Neuroscience, III. Institute of Physics - Biophysics, University of Göttingen, Göttingen, Germany.
Biophysics and Systems Biology Section, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay.
Sci Rep. 2023 Jan 19;13(1):1089. doi: 10.1038/s41598-023-27809-8.
Mechanisms that ensure the stability of dynamical systems are of vital importance, in particular in our globalized and increasingly interconnected world. The so-called connectivity-stability dilemma denotes the theoretical finding that increased connectivity between the components of a large dynamical system drastically reduces its stability. This result has promoted controversies within ecology and other fields of biology, especially, because organisms as well as ecosystems constitute systems that are both highly connected and stable. Hence, it has been a major challenge to find ways to stabilize complex systems while preserving high connectivity at the same time. Investigating the stability of networks that exhibit small-world or scale-free topology is of particular interest, since these topologies have been found in many different types of real-world networks. Here, we use an approach to stabilize recurrent networks of small-world and scale-free topology by increasing the average self-coupling strength of the units of a network. For both topologies, we find that there is a sharp transition from instability to asymptotic stability. Then, most importantly, we find that the average self-coupling strength needed to stabilize a system increases much slower than its size. It appears that the qualitative shape of this relationship is the same for small-world and scale-free networks, while scale-free networks can require higher magnitudes of self-coupling. We further explore the stabilization of networks with Kronecker-Leskovec topology. Finally, we argue that our findings, in particular the stabilization of large recurrent networks through small increases in the unit self-regulation, are of practical importance for the stabilization of diverse types of complex systems.
确保动力系统稳定性的机制至关重要，特别是在我们全球化和日益互联的世界中。所谓的连通稳定性困境表示理论发现，即大型动力系统组件之间的连通性增加会大大降低其稳定性。这一结果在生态学和其他生物学领域引发了争议，尤其是因为生物体和生态系统构成了高度连接且稳定的系统。因此，如何在保持高连通性的同时稳定复杂系统一直是一个主要挑战。研究具有小世界或无标度拓扑的网络的稳定性特别有趣，因为这些拓扑结构已经在许多不同类型的真实网络中被发现。在这里，我们通过增加网络单元的平均自耦合强度来稳定具有小世界和无标度拓扑的递归网络。对于这两种拓扑结构，我们发现从不稳定到渐近稳定存在一个明显的转变。然后，最重要的是，我们发现稳定系统所需的平均自耦合强度的增加速度远低于其大小。似乎这种关系的定性形状对于小世界和无标度网络是相同的，而无标度网络可能需要更高的自耦合强度。我们进一步探索了 Kronecker-Leskovec 拓扑的网络稳定化。最后，我们认为我们的发现，特别是通过小幅度增加单元自我调节来稳定大型递归网络，对于稳定各种类型的复杂系统具有实际意义。
