Tang Yang, Wang Zidong, Fang Jian-an
College of Information Science Technology, Donghua University, Shanghai, China.
Chaos. 2009 Mar;19(1):013112. doi: 10.1063/1.3068350.
In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter beta, the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks.
在本文中，我们考虑分数阶加权复杂动态网络的牵制控制问题。被充分研究的整数阶复杂网络是分数阶网络的特殊情况。所考虑的网络模型可以表示有向和无向加权网络。首先，基于特征值分析和分数阶稳定性理论，推导了此类牵制分数阶网络的一些局部稳定性性质，并估计了有效的稳定区域。一个令人惊讶的发现是，分数阶复杂网络可以通过降低分数阶q来实现自身稳定，而无需牵制任何节点。其次，详细介绍了分数阶复杂网络的数值算法。最后，在无标度复杂网络中进行了数值模拟，结果表明分数阶q越小、控制增益矩阵D越大、可调权重参数β越大、整体耦合强度c越大，牵制方案就越有可能具备增强分数阶复杂网络控制性能的能力。
