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Adaptive Topologies

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Controlling Synchronization Patterns in Complex Networks

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Abstract

The previous chapter introduced a new method to control cluster synchronization by adaptively tuning \(\beta \), the phase of the complex coupling strength \(\sigma =K\exp (i\beta )\).

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Notes

  1. 1.

    In the previous chapters, I discussed that each M-state might, depending on M and the number of nodes N, correspond to several different states with different m where m neighboring nodes, i.e., \(\varphi _{(i+1)\mathrm{mod}N}-\varphi _i=2\pi m/N\), and M relates to m according to \( M = \text{ lcm }(m, N )/m\) (see Sect. 5.2). Recall that lcm stands for the least common multiplier. Here, the different m states for the same M cannot be distinguished any longer because the term “neighboring nodes” is not well defined in a topology which is not a regular ring network. Thus, in the following, I will only distinguish between different M but not m.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Judith Lehnert

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  1. Judith Lehnert
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Correspondence to Judith Lehnert .

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Lehnert, J. (2016). Adaptive Topologies. In: Controlling Synchronization Patterns in Complex Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-25115-8_10

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