Now showing items 1-7 of 7
Nonlinear Analogue of the May-Wigner Instability Transition
We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing ...
Explosive higher-order Kuramoto dynamics on simplicial complexes
(American Physical Society, 2020)
The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However the existing dynamical models defined on simplicial ...
Counting equilibria of large complex systems by instability index
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction ...
Higher-order simplicial synchronization of coupled topological signals
(Nature Research, 2021-06-07)
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order ...
Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions
(Nature Research (part of Springer Nature), 2021)
When describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis ...
Dirac synchronization is rhythmic and explosive
Geometry, Topology and Simplicial Synchronization
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral ...