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.

我们考虑根据不同规律随时间演化的动态单元网络，并以高度不规则的方式相互耦合。研究如何引导此类系统的动力学朝着期望的演化方向发展，在许多科学领域都具有很大的实际意义，并且可以深入了解网络结构和动态行为之间的相互作用。我们提出了一种固定协议，用于在网络系统上施加与运动方程兼容的特定动态演化。该方法不对局部动力学施加任何限制，局部动力学可能因节点而异，也不对节点之间的相互作用施加任何限制，其原则上可以采用任何非线性数学形式并由加权、有向或无向链路表示。我们首先在混沌振荡器的小型合成网络上探索我们的方法，这使我们能够揭示固定节点的有序序列与其在网络中的拓扑影响之间的相关性。然后我们考虑一个包含 12 种物种的营养网，它是哺乳动物食物网的模型。通过固定相对较少数量的物种，我们可以使系统放弃从（通常不受控制的）初始状态向目标动态的自发演化，或者定期控制它以使种群在规定的范围内演化。讨论了这些发现与环境管理和保护的相关性。