Abstract
The nodes of the network are composed of the spatiotemporal chaos systems. The relations between the nodes are built through a weighted connection and the nonlinear terms of the chaos systems themselves are taken as coupling functions. The structure of the coupling functions between the connected nodes and the range of the control gain are obtained based on Lyapunov stability theory. It is proven that generalized chaos synchronization of the weight complex network can be realized even if the coupling strength between the nodes is adopted as any weight value. Subsequently, the catalytic reaction diffusion system which has spatiotemporal chaos behavior is taken as example, and simulation results show the effectiveness of the synchronization principle.
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References
Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001)
Watts, D.J., Strogatz, S.H.: Collective dynamics of “small world” networks. Nature 393, 440–442 (1998)
Albert, R., Jeong, H., Barabási, A.L.: Diameter of the world-wide web. Nature 401, 130–131 (1999)
Huberman, B.A., Adamic, L.A.: Growth dynamics of the world-wide web. Nature 401, 131 (1999)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Adamic, L.A., Huberman, B.A.: Power-law distribution of the world wide web. Science 287, 2115 (2000)
Huang, L., Park, K., Lai, Y.C., Yang, L., Yang, K.Q.: Abnormal synchronization in complex clustered networks. Phys. Rev. Lett. 97, 164101 (2006)
Li, X.: Uniform synchronous criticality of diversely random complex networks. Physica A 360, 629–636 (2006)
Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S., Gilles, E.D.: Metabolic network structure determines key aspects of functionality and regulation. Nature 420, 190–193 (2002)
Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)
Ravasz, E., Barabási, A.L.: Hierarchical organization in complex networks. Phys. Rev. E 67, 026112 (2003)
Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Large-scale topological and dynamical properties of the Internet. Phys. Rev. E 65, 066130 (2002)
Haken, H.: Synchronization and pattern recognition in a pulse-coupled neural net. Physica D 205, 1–6 (2005)
Timme, M., Wolf, F., Geisel, T.: Topological speed limits to network synchronization. Phys. Rev. Lett. 92, 074101 (2004)
Motter, A.E., Zhou, C., Kurths, J.: Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E 71, 016116 (2005)
Lu, W., Chen, T.: Synchronization analysis of linearly coupled networks of discrete time systems. Physica D 198, 148–168 (2004)
Atay, F.M., Jost, J., Wende, A.: Delays, connection topology, and synchronization of coupled chaotic maps. Phys. Rev. Lett. 92, 144101 (2004)
Lü, J.H., Yu, X.H., Chen, G.R.: Chaos synchronization of general complex dynamical networks. Physica A 334, 281–302 (2004)
Han, X.P., Lu, J.A.: The changes on synchronization ability of coupled networks from ring networks to chain networks. Sci. Chin. F 50, 615–624 (2007)
Yu, W.W., Cao, J.D.: Synchronization control of stochastic delayed neural networks. Physica A 373, 252–260 (2007)
Hennig, D., Schimansky-Geier, L.: Implications of heterogeneous inputs and connectivity on the synchronization in excitable networks. Physica A 387, 967–981 (2008)
Hung, Y.C., Huang, Y.T., Ho, M.C., Hu, C.K.: Paths to globally generalized synchronization in scale-free networks. Phys. Rev. E 77, 016202 (2008)
Barrat, A., Barthélemy, M., Vespignani, A.: Weighted evolving networks: coupling topology and weight dynamics. Phys. Rev. Lett. 92, 228701 (2004)
Li, W., Cai, X.: Statistical analysis of airport network of China. Phys. Rev. E 69, 046106 (2004)
Fang, J.Q., Bi, Q., Li, Y., Lu, X.B., Liu, Q.: A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks. Sci. Chin. G 50, 379–396 (2007)
Xiang, L.Y., Liu, Z.X., Chen, Z.Q., Yuan, Z.Z.: Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers. Sci. Chin. F 51, 511–523 (2008)
Lü, L.: Nonlinear Dynamics and Chaos. Dalian Publishing House, Dalian (2000)
Lynch, D.T.: Chaotic behavior of reaction systems: mixed cubic and quadratic autocatalysis. Chem. Eng. Sci. 47, 4435–4444 (1992)
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Lü, L., Li, C. Generalized synchronization of spatiotemporal chaos in a weighted complex network. Nonlinear Dyn 63, 699–710 (2011). https://doi.org/10.1007/s11071-010-9831-2
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DOI: https://doi.org/10.1007/s11071-010-9831-2