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Feasibility and stability in large Lotka Volterra systems with interaction structure
Xiaoyuan Liu1, George W A Constable1, Jonathan W Pitchford1
1Department of Mathematics, University of York, York, YO10 5DD, United Kingdom.
Abstract:
Complex system stability can be studied via linear stability analysis using random matrix theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalized Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.
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