Abstract
In this chapter, we show by theoretical analysis and computer simulations that a plethora of novel patterns can be generated by multiplexing adaptive networks. The concept of lifted states is introduced in order to distinguish between new states from multilayer manifestations of single layer states. We develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. We illustrate our findings by using a phase oscillator model which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.
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Berner, R. (2021). Multilayered Adaptive Networks. In: Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-74938-5_8
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DOI: https://doi.org/10.1007/978-3-030-74938-5_8
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