Pinning control of scale-free complex networks

The pinning control strategy, including specifically pinning scheme and randomly pinning scheme, is used to stabilize scale-free networks in this paper. A scale-free dynamical network model is first introduced and then, based on this model, a stability condition is derived in terms of a linear matrix inequality. Finally, a numerical simulation example is provided to verify the theoretical results.

[1]  K. Kaneko Coupled Map Lattice , 1991 .

[2]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[3]  Carson C. Chow,et al.  Small Worlds , 2000 .

[4]  S. Strogatz Exploring complex networks , 2001, Nature.

[5]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[6]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[7]  L. Chua Cnn: A Paradigm for Complexity , 1998 .

[8]  Gesine Reinert,et al.  Small worlds , 2001, Random Struct. Algorithms.

[9]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[10]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[11]  Yuhai Tu,et al.  How robust is the Internet? , 2000, Nature.

[12]  Béla Bollobás,et al.  Random Graphs , 1985 .