Category: Ecology

Summary: Finding the minimum recycling-buffer strength needed to restabilize a trophically coherent consumer-resource community after mismatch-driven destabilization.

Nutrient recycling can stabilize ecological communities, but it is not obvious how much recycling is needed once elemental mismatch has already pushed the system into instability. This experiment asks for the minimum rescue strength required to recover linear stability in a trophically coherent consumer-resource community.

The script constructs dense non-symmetric Jacobians for random trophically coherent communities with fixed mismatch in the unstable regime. It then uses GPU eigensolves, iterative deepening, and bisection on recycling-buffer strength to locate the restabilization threshold.

That cleanly isolates recycling as a rescue mechanism rather than a background feature of the model. The output is a finite-size spectral map of how much buffering is needed to undo a known destabilizing stress.

Method: GPU dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on recycling-buffer strength at fixed mismatch.

What is measured: Critical recycling-buffer threshold, leading-eigenvalue stability boundary, restabilization status, and bracket width.