Gianluigi Mongillo | Searcharxiv

arXiv2026

On the relationship between equilibria and dynamics in large, random neuronal networks

We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with an extensive, but fractionally-small, number of unstable directions. Despite network's connectivity being completely random, the equilibria are strongly correlated and, as a result, they occupy a small region in the phase space. The attractor is inside this region. This geometry explains why the chaotic dynamics in these models can be described by a fractionally-small number of collective modes.

cond-mat.dis-nn↗

arXiv2025

Is the cortical dynamics ergodic? A numerical study in partially symmetric networks of spiking neurons

Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not understood. Here, we show that slow dynamics naturally and robustly emerges in dynamically-balanced networks of spiking neurons. This requires only partial symmetry in the synaptic connectivity, a feature of local cortical networks observed in experiments. The symmetry generates an effective, excitatory self-coupling of the neurons that leads to long-lived fluctuations in the network activity, without destroying the dynamical balance. When the excitatory self-coupling is suitably strong, the same mechanism leads to multiple equilibrium states of the network dynamics. Our results reveal a novel dynamical regime of the collective activity in spiking networks, where the memory of the initial state persists for very long times and ergodicity is broken.

cond-mat.dis-nn↗