Same Resident Strains, Different Attractors: Opposite Local Growth Signs for a Rare Third Strain

What the math gives to ML

The paper provides a transferable mechanism: identical parameters can support multiple locally attracting resident states, including an equilibrium and a periodic orbit, while the same rare perturbation has opposite initial growth signs around those attractors. The invasion criterion is a weighted sum of host-history fractions minus removal, with the periodic-orbit analogue given by a Floquet exponent obtained by averaging the instantaneous rare-strain growth rate over one cycle. In neural networks, this can become an attractor-conditioned stability probe and regularizer for recurrent or state-space models, explicitly testing whether small hidden-state perturbations grow differently in different long-term regimes. The key falsifiable prediction is that local perturbation growth, Jacobian spectra, or Floquet multipliers will be basin-dependent even when model parameters and inputs are identical.