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Updated: Oct 13, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Double transitions and hysteresis in heterogeneous contagion processes
Joongjae Kook1, Jeehye Choi2, Byungjoon Min1,2
1Department of Physics, Chungbuk National University, Cheongju, Chungbuk 28644, Korea.
Abstract:
In many real-world contagion phenomena, the number of contacts to spreading entities for adoption varies for different individuals. Therefore, we study a model of contagion dynamics with heterogeneous adoption thresholds. We derive mean-field equations for the fraction of adopted nodes and obtain phase diagrams in terms of the transmission probability and fraction of nodes requiring multiple contacts for adoption. We find a double phase transition exhibiting a continuous transition and a subsequent discontinuous jump in the fraction of adopted nodes because of the heterogeneity in adoption thresholds. Additionally, we observe hysteresis curves in the fraction of adopted nodes owing to adopted nodes in the densely connected core in a network.
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