Abstract
This paper investigates the pinning control schemes and corresponding criteria for group synchronization in a complex dynamical network with different types of chaotic oscillators. We present the linear pinning and adaptive pinning control schemes to make different groups of oscillators synchronize to their own synchronization states, respectively. The globally asymptotically stable criteria for group synchronization are derived, which indicate that the group synchronization can be realized only by pinning a part of nodes in a general network. Finally, some numerical simulations are provided to verify the theoretical results.
Highlights
Nowadays, complex networks widely exist in nature and society, such as the World Wide Web, the Internet, traffic network, communication network, power network, and social network
This paper investigates the pinning control schemes and corresponding criteria for group synchronization in a complex dynamical network with different types of chaotic oscillators
We present the linear pinning and adaptive pinning control schemes to make different groups of oscillators synchronize to their own synchronization states, respectively
Summary
Complex networks widely exist in nature and society, such as the World Wide Web, the Internet, traffic network, communication network, power network, and social network. In [15], we presented a complex dynamical network model with M groups of different chaotic oscillators and derived some criteria to guarantee the group synchronization for a linearly or adaptively coupled network, respectively, under the “same input” condition. Zhou et al presented a simple approximate formula for estimating the detailed number of pinning nodes and the magitude of the coupling strength for a given general complex dynamical network in [19]. The researchers mentioned above focused on Mathematical Problems in Engineering the global synchronization of complex dynamical networks by pinning control. We will use the pinning control schemes to realize the group synchronization in a general complex dynamical network. Different from [15], this work mainly focuses on the pinning control schemes and the corresponding criteria to realize the group synchronization in a complex dynamical network.
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