论文标题

转向复杂的网络朝着所需的动态

Steering complex networks toward desired dynamics

论文作者

Gutiérrez, Ricardo, Materassi, Massimo, Focardi, Stefano, Boccaletti, Stefano

论文摘要

我们考虑根据不同定律随时间发展的动力单元网络,并以高度不规则的方式相互耦合。在许多科学领域,研究如何将这种系统的动态转向所需的进化具有极大的实际兴趣,并提供了对网络结构与动态行为之间相互作用的见解。我们提出了一个固定协议,以施加与网络系统上运动方程兼容的特定动态演变。该方法不对局部动力学施加任何限制,这些动力可能会因节点到节点而异,也不对节点之间的相互作用有所不同,而节点之间的相互作用可能在原则上采用任何非线性数学形式,并由加权,定向或无方向的链接表示。我们首先探讨了混乱振荡器的小型合成网络的方法,这使我们能够在固定节点的有序序列与网络中其拓扑影响之间建立相关性。然后,我们考虑一个12种营养网络网络,该网络是哺乳动物网络的模型。通过将相对较少的物种固定,可以使系统从其(通常不受控制的)初始状态(通常是不受控制的)初始状态放弃其自发进化,或者定期控制其以使种群在规定的范围内进化。讨论了这些发现与环境管理和保护的相关性。

We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great practical interest in many areas of science, as well as providing insight into the interplay between network structure and dynamical behavior. We propose a pinning protocol for imposing specific dynamic evolutions compatible with the equations of motion on a networked system. The method does not impose any restrictions on the local dynamics, which may vary from node to node, nor on the interactions between nodes, which may adopt in principle any nonlinear mathematical form and be represented by weighted, directed or undirected, links. We first explore our method on small synthetic networks of chaotic oscillators, which allows us to unveil a correlation between the ordered sequence of pinned nodes and their topological influence in the network. We then consider a 12-species trophic web network, which is a model of a mammalian food web. By pinning a relatively small number of species, one can make the system abandon its spontaneous evolution from its (typically uncontrolled) initial state towards a target dynamics, or periodically control it so as to make the populations evolve within stipulated bounds. The relevance of these findings for environment management and conservation is discussed.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源