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Results for Global Attractivity of Interior Equilibrium Points for Lotka-Volterra Systems
arXiv:2512.11384v1 Announce Type: cross
Abstract: This paper provides global attractivity results for the interior equilibrium point of a general Lotka-Volterra system with no restriction on the dimension of the system and with no special structure or properties of the interaction matrix. The main result contains as special cases all known general results, including the Volterra-Lyapunov theorem and the recently proposed eigenvector conditions. Moreover, global attractivity of the interior equilibrium point is shown for a three-dimensional example, where none of the existing general results can be applied.
Abstract: This paper provides global attractivity results for the interior equilibrium point of a general Lotka-Volterra system with no restriction on the dimension of the system and with no special structure or properties of the interaction matrix. The main result contains as special cases all known general results, including the Volterra-Lyapunov theorem and the recently proposed eigenvector conditions. Moreover, global attractivity of the interior equilibrium point is shown for a three-dimensional example, where none of the existing general results can be applied.
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