Category: Neuroscience

Summary: Finding the minimum reciprocal excitatory-inhibitory motif strength needed to restabilize a Dale-law network destabilized by clustered inhibition.

Neuronal networks constrained by Dale's law can become unstable when inhibition is clustered in ways that create strongly structured feedback. This experiment asks whether adding reciprocal excitatory-inhibitory motifs can rescue such a network, and if so, how strong those motifs must be before stability returns.

The model generates dense non-symmetric random-network matrices in a fixed unstable regime and then bisects the reciprocal-motif parameter while carrying the surviving bracket to larger system sizes. Full eigensolves identify the point where the dominant spectral mode crosses back into the stable region.

That provides a quantitative view of a motif-level repair mechanism. Instead of asking whether reciprocity changes spectra in principle, the experiment estimates the minimum reciprocal structure needed to undo a specific destabilizing pattern under Dale-law constraints.

Method: Dense non-symmetric eigensolves with iterative deepening and bisection on reciprocal excitatory-inhibitory motif strength in Dale-law networks.

What is measured: Critical reciprocal-motif rescue threshold, leading eigenvalue, stability restoration status, system size reached, and bracket width.