Now showing items 1-3 of 3
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 ...
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 ...
The topological Dirac equation of networks and simplicial complexes
(IOP Publishing, 2021-09-14)
We define the topological Dirac equation describing the evolution of a topological wave function on networks or on simplicial complexes. On networks, the topological wave function describes the dynamics of topological ...