Global Stability of a Discrete Population Dynamics Model with Two Delays

  • Authors:

  • R. M. Nigmatulin

  • Affiliations:

  • Chelyabinsk State Pedagogical University, Chelyabinsk, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2005

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Abstract

A population dynamics model $$x_n = \frac{{\alpha x_{n - m} }}{{1 + x_{n - m} + \beta x_{n - k} }}$$ with two delays k and m and coefficients 驴 1 and β 驴 0 is studied. A sufficient condition, which is also necessary for certain delays, for the global asymptotic stability of the stationary solution $$x_n = \frac{{\alpha - 1}}{{\beta + 1}}$$ is formulated.