Abstract
The authors study the control of cluster synchronization in regular networks by the scheme of pinning couplings. The authors show numerically and mathematically that by changing the number and locations of the pinning nodes, a regular network can be controlled to different cluster synchronization states. This study shows the flexibility of regular networks in generating cluster synchronization, and highlights, from a different perspective, the importance of network symmetry on cluster synchronization.
Highlights
Cluster synchronization (CS), known as partial or group synchronization, refers to the coherent motion of partial oscillators in large-size systems [1], which, for its significant implications to the functionalities of many natural and manmade systems, has been extensively studied by researchers from different fields over the past two decades [2,3,4,5,6,7,8,9,10]
We would like to point out the difference between the current study and the previous ones on the pinning control of synchronization in complex networks
Different from previous studies in which the mission of the control is to synchronize all nodes in the network to an external controller [35,37,38], the present work concentrates on how to control a network to different CS states of spatial structures
Summary
Cluster synchronization (CS), known as partial or group synchronization, refers to the coherent motion of partial oscillators in large-size systems [1], which, for its significant implications to the functionalities of many natural and manmade systems, has been extensively studied by researchers from different fields over the past two decades [2,3,4,5,6,7,8,9,10]. If the network nodes are partially pinned, it is highly possible that the node partitions will be different from the original partitions In such a case, the desired CS state will no longer be a solution of the system dynamics, making the control failed. It is worth mentioning that in previous studies, the mission of pinning control is mainly focused on driving the whole network from the desynchronization state to the global synchronization state In such a case, as the controller is coupled unidirectionally to a fraction of nodes in the network, the manifold of the global synchronization state is defined by the trajectory of the controller. When the targets are CS states, the synchronization manifolds are no longer defined by the controller, but are dependent on the network symmetries In this case, the conventional MSF cannot be applied directly and a generalized method should be employed.
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