Global Asymptotic Stability in Kolmogorov Systems that Characterize Tridimensional Lotka–Volterra Systems

• Érika Diz-Pita ^[1]
  1. [1] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper we deal with the problem of determining when a class of planar polynomial differential systems is globally asymptotically stable. Systems with this property play a central role in the qualitative theory of differential equations, as it guarantees a predictable asymptotic behavior of solutions. The system considered here is the Kolmogorov system ˙ x = x(a0 + a1x + a2z2 + a3z), ˙z = z(c0 + c1x + c2z2 + c3z), and it arises in the study of tridimensional Lotka–Volterra equations. Our objective is to obtain a complete characterization of the conditions for which the origin of this system is globally asymptotically stable. To achieve this goal,we use desingularization blow-up techniques and we study the behavior at infinity by means of the Poincaré compactification.

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