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

TL;DR

This study demonstrates that partial symmetry in cortical networks of spiking neurons induces slow, long-lived fluctuations and multiple equilibrium states, breaking ergodicity and explaining prolonged cortical activity.

Contribution

It reveals that partial symmetry in synaptic connectivity leads to slow dynamics and multiple states, a novel mechanism for cortical activity patterns.

Findings

Slow dynamics emerge naturally in partially symmetric networks.

Symmetry induces long-lived fluctuations in network activity.

Multiple equilibrium states occur when excitatory self-coupling is strong.

Abstract

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.