Kirchhoff Migration, Slow--Fast Reduction, and Volterra--Lyapunov Functions in Spatial Fisheries, as Applications of Jacobian Triangularity on Siphon Faces
Year: 2026
Type: preprint
Abstract: Animal movement among fishing grounds, protected areas and habitat fragments is often fast compared with growth and harvesting. We study multi-patch models with fast migration, described by irreducible Kirchhoff matrices. The main results are: (1) invasion exponents at boundary equilibria equal Perron-weighted averages of local growth rates to leading order, with explicit second-order corrections, so invasion signs and local stability transfer from the reduced to the full system (singular perturbation and Perron--Frobenius theory, organised by siphon faces); (2) for Schaefer fisheries, the connected maximum sustainable yield is bounded by the sum of isolated yields, and optimal migration under corridor-rate limits is a convex quadratic program; (3) connecting patches can let a predator persist although it cannot persist on any isolated patch, and saturating predation can destabilize coexistence while invasion remains possible; (4) for several predator stocks sharing one prey, a single Volterra identity decides which stock survives and bounds the catch of the losing stocks, including at every migration speed for balanced migration; (5) an extension to consumers sharing recycled resources, building on the microbial consumer--resource model of Faul, Richard, Van der Meer and Mazza.
Source: Preprints.org
Authors: Florin Avram, Ali Moussaoui
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225312847