Fundamental interactions in self-organized critical dynamics on higher-order networks
arxiv(2024)
摘要
In functionally complex systems, higher-order connectivity is often revealed
in the underlying geometry of networked units. Furthermore, such systems often
show signatures of self-organized criticality, a specific type of
non-equilibrium collective behaviour associated with an attractor of internal
dynamics with long-range correlations and scale invariance, which ensures the
robust functioning of complex systems, such as the brain. Here, we highlight
the intertwining of features of higher-order geometry and self-organized
critical dynamics as a plausible mechanism for the emergence of new properties
on a larger scale, representing the central paradigm of the physical notion of
complexity. Considering the time scale of the structural evolution with the
known separation of the time scale in self-organized criticality, i.e.,
internal dynamics and external driving, we distinguish three classes of
geometries that can shape the self-organized dynamics on them differently. We
provide an overview of current trends in the study of collective dynamics
phenomena, such as the synchronization of phase oscillators and discrete spin
dynamics with higher-order couplings embedded in the faces of simplicial
complexes. For a representative example of self-organized critical behaviour
induced by higher-order structures, we present a more detailed analysis of the
dynamics of field-driven spin reversal on the hysteresis loops in simplicial
complexes composed of triangles. These numerical results suggest that two
fundamental interactions representing the edge-embedded and triangle-embedded
couplings must be taken into account in theoretical models to describe the
influence of higher-order geometry on critical dynamics.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要