Liouvillian and Analytic Integrability of a Generalized Gause System

• Jorge A. Borrego-Morell ^[1]
  1. [1] Universidade Federal do Rio de Janeiro

     Universidade Federal do Rio de Janeiro

     Brasil

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 3, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this work, we identify the regions of the parameter space in which a predator–prey system-derived from the classical Gause model with a generalized Holling response function and logistic prey growth in the absence of predators-fails to be Liouvillian integrable. Although the model parameters have biological meaning only when restricted to appropriate real domains, our analysis is carried out in the complex setting, which provides a unified algebraic framework; the resulting nonintegrability conditions remain valid in the biologically relevant regime. As a consequence, we establish the nonintegrability of an Abel differential equation of the second kind with polynomial coefficients obtained from the system. Finally, we analyze the existence of a local analytic first integral in neighborhoods of the equilibrium points.

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