Stability and Hopf Bifurcation Analysis for a Two-Species Commensalism System with Delay

• Li, Tianyang ^[1] ; Wang, Qiru ^[1]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
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• Resumen

  • This paper is devoted to studying the dynamics of a two-species commensalism system with delay. By analyzing the characteristic equation and regarding the time delay as the bifurcation parameter, we investigate the local asymptotic stability of the positive equilibrium and show the existence of periodic solutions bifurcating from the positive equilibrium. Then, we derive the precise formulae to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions by using the normal form theory and the center manifold theorem. Numerical simulation results are also included to support our theoretical analysis.