A dynamical network achieves generalized synchronization if there exists an asymptotically stable manifold in which the solution of each node is uniquely determined as a static function of the states of any other node in the network. For bidirectionally coupled networks, the description of a synchronization manifold changes from pairwise-explicit form to an implicit form of the relationship between its nodes. Using this description, we start with a network of identical nodes that can be controlled towards a synchronization manifold, for this bidirectionally coupled network we propose a pinning strategy to impose a desired relation between nodes based on invertible coordinate transformations. We illustrate our results with numerical simulations of well-known chaotic benchmark systems.

如果存在一个渐近稳定的流形，其中每个节点的解被唯一确定为网络中任何其他节点状态的静态函数，那么动态网络就实现了广义同步。对于双向耦合网络，同步流形的描述从成对显式形式变为其节点之间关系的隐式形式。使用这个描述，我们从可以控制同步流形的相同节点网络开始，对于这个双向耦合网络，我们提出了一种钉扎策略，以基于可逆坐标变换在节点之间施加所需的关系。我们用著名的混沌基准系统的数值模拟来说明我们的结果。