Stable equilibria in the Lotka-Volterra equations

2025/12/15 by Magnus Aspenberg, Aspenberg, Magnus, Erik A. Martens +3
Mathematics · Medicine · #37N25 #92-10 #92D25 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.2512.13347

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y. Takeuchi, and H. Tokumaru, who, in a series of papers, give sufficient (and for some cases necessary) conditions for the existence of a stable equilibrium point.

Citations

• Equilibrium and surviving species in a large Lotka-Volterra system of differential equations
• Global Stability in Many-Species Systems

Related

• A Locally Stable Equilibria Criterion for the Generalized Lotka-Volterra
• Convergence to equilibrium in competitive Lotka-Volterra equations
• Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system
• Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions
• New stability criteria for periodic planar Lotka-Volterra systems