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Samuel Unicomb1, Gerardo Iñiguez2,3, Márton Karsai4

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Weighted networks are crucial for understanding complex systems. This study models threshold dynamics on these networks, revealing how weight variations non-monotonously affect cascade emergence times.

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Area of Science:

  • Complex systems science
  • Network science
  • Dynamical systems

Background:

  • Weighted networks represent systems where interaction strength is critical.
  • Link weights in networks influence node behavior, essential for processes like social contagion and neural firing.
  • Modeling threshold dynamics on weighted networks has been an under-explored area.

Purpose of the Study:

  • To investigate threshold dynamics on weighted networks.
  • To analyze the impact of weight heterogeneity on cascade emergence.
  • To develop a methodology applicable to various binary state processes.

Main Methods:

  • Utilized numerical and analytical tools.
  • Studied a dynamical threshold model on synthetic and real-world weighted networks.
  • Examined the effects of varying weight distributions and network structures.

Main Results:

  • Cascade emergence time shows a non-monotonous dependence on weight heterogeneity.
  • Weight variations can accelerate or decelerate cascade dynamics.
  • Identified non-trivial parameter spaces influenced by network type and weight distributions.

Conclusions:

  • Weight heterogeneity plays a significant role in threshold dynamics on complex networks.
  • The developed methodology can be applied to diverse binary state processes.
  • Understanding edge heterogeneities is crucial for various natural and social phenomena.