@article{Wang2026, 
author = {Louis Shuo Wang and Jiguang Yu},
title = {Algebraic–spectral thresholds and discrete–continuous stability transfer in Leslie–Gower systems},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {1},
pages = {251-290},
keywords = {algebraic elimination, saddle–node and Hopf bifurcation, Euler discretization, intraguild predation},
url = {https://www.sciopen.com/article/10.3934/era.2026013},
doi = {10.3934/era.2026013},
abstract = {We studied an intraguild–predation system where an intermediate consumer and a top consumer exploit a shared basal resource. A compact nondimensionalization yielded five interpretable parameters—relative predator growth    α, crowding    β, enrichment    γ, and depletion couplings    δ  ,  ε. We presented closed-form thresholds that organize the dynamics: the coexistence equilibrium exists exactly when a quadratic in the resource steady state has a root in    (  0  ,  β  ); as    γ varies, a two-equilibria window appears and terminates at an explicit saddle–node value        γ    1    +  , with transversality confirmed and transcritical/pitchfork alternatives excluded. A Hopf onset criterion was given via the characteristic polynomial coefficients along the interior branch. For the forward-Euler discretization we established positivity, an absorbing set under an explicit stepsize bound, and stability tests that reduce to        |    1  +  Δ  τ  λ      |    =  1. Extensions to diffusion and stochastic forcing suggest the incorporation of more realistic spatial and stochastic factors. The thresholds were directly calibratable, enabling reproducible, mechanistic predictions for applied systems.}
}