摘要We present a network model with a new coupled scheme which is the generalization of drive-response systems called a drivingly coupled network. The synchronization of the network is investigated by numerical simulations based on Lorenz systems. By calculating the largest transversal Lyapunov exponents of such network, the stable and unstable regions of synchronous state for eigenvalues in such network can be obtained and many kinds of drivingly coupled arrays based on Lorenz systems such as all-to-all, star-shape, ring-shape and chain-shape networks are considered.
Abstract:We present a network model with a new coupled scheme which is the generalization of drive-response systems called a drivingly coupled network. The synchronization of the network is investigated by numerical simulations based on Lorenz systems. By calculating the largest transversal Lyapunov exponents of such network, the stable and unstable regions of synchronous state for eigenvalues in such network can be obtained and many kinds of drivingly coupled arrays based on Lorenz systems such as all-to-all, star-shape, ring-shape and chain-shape networks are considered.
[1] Watts D J and Strogatz S H 1998 Nature 391 440 [2] Barabasi A L and Albet R 1999 Science 286 509 [3] Wang X F and Chen G 2002 Int. J. Bifur. Chaos 12 187 [4] Wang X F and Chen G 2002 IEEE Trans. Circuits Syst. I 49 54 [5] L\"{u J H and Chen G 2005 IEEE Trans. Auto. Control. 50 841 [6] Zhou J, Lu J A and L\"{u J H 2006 IEEE Trans.Auto. Control 51 652 [7] Pecora L M and Carroll T C 1990 Phys. Rev. Lett. 64 821 [8] Pecora L M and Carroll T C 1991 Phys. Rev. A 442374 [9] Pecora L M and Carroll T C 1998 Phys. Rev. Lett. 80 2109 [10] Yang J and Hu G 1998 Phys. Rev. Lett. 80 496