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Attracting Complex Networks

In: Complex Networks and Dynamics

Author

Listed:
  • G. Guerrero

    (Universidad Central del Ecuador)

  • J. A. Langa

    (Seville University)

  • A. Suárez

    (Seville University)

Abstract

Real phenomena from different areas of Life Sciences can be described by complex networks, whose structure is usually determining their intrinsic dynamics. On the other hand, Dynamical Systems Theory is a powerful tool for the study of evolution processes in real situations. The concept of global attractor is the central one in this theory. In the last decades there has been an intensive research in the geometrical characterization of global attractors. However, there still exists a weak connection between the asymptotic dynamics of a complex network and the structure of associated global attractors. In this paper we show that, in order to analyze the long-time behavior of the dynamics on a complex network, it is the topological and geometrical structure of the attractor the subject to take into account. In fact, given a complex network, a global attractor can be understood as the new attracting complex network which is really describing and determining the forwards dynamics of the phenomena. We illustrate our discussion with models of differential equations related to mutualistic complex networks in Economy and Ecology.

Suggested Citation

  • G. Guerrero & J. A. Langa & A. Suárez, 2016. "Attracting Complex Networks," Lecture Notes in Economics and Mathematical Systems, in: Pasquale Commendatore & Mariano Matilla-García & Luis M. Varela & Jose S. Cánovas (ed.), Complex Networks and Dynamics, pages 309-327, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-40803-3_12
    DOI: 10.1007/978-3-319-40803-3_12
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    Cited by:

    1. Galadí, J.A. & Soler-Toscano, F. & Langa, J.A., 2022. "Model transform and local parameters. Application to instantaneous attractors," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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