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Christian Kluge

Publications and source records attributed to Christian Kluge.

2 recordsLinked to original sources
arXiv2026

Cascades on Networks with Functional Structure

We consider a version of the Watts threshold model on directed multiplex configuration model networks, and present a detailed analysis of the cascade size, single-seed cascade probability and cascade condition. We then introduce a smaller class of network models that we call "constrained multiplex networks", which is designed to represent networks with so-called "functional" or "complementary" structure. We find that the particular choice of functional structure affects the phase transitions of the cascade model in a variety of ways.

nlin.AO↗
arXiv2026

Symmetry-Breaking and Hysteresis in a Duplex Voter Model

We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that state on the other layer. Despite the model's simplicity, our mathematical analysis reveals a rich phase diagram that includes spontaneous symmetry-breaking and a cusp bifurcation, which arises when noise is introduced into the model. In particular, this bifurcation mechanism can be viewed as a prototypical unfolding of the change between explosive and non-explosive transitions observed in various other network models. We cross-validate our analytic results by numerical simulations.

nlin.AO↗