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September 17, 2025Mathematics5 citationsOpen Access

Basins of Attraction for Third-Order Sigmoid Beverton Holt Difference Equation

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MKM. R. S. KulenovićRSRyan C. Sullivan

Key Points

  • The study identifies and describes the basins of attraction for multiple equilibrium points.
  • Results highlight the existence of period-two and period-three solutions within the system dynamics.
  • This involves analyzing a third-order difference equation relevant for modeling population dynamics.
  • The implications of these findings may enhance understanding of complex behavior in ecological models.

Abstract

The third-order difference equation yn+1=a1yn21+yn2+a2yn−121+yn−12+a3yn−221+yn−22, as a potential discrete time model of population dynamics with three generation involved, is studied. The parts of the basins of attraction of three equilibrium points that this equation admits are described. Some results about period-two and period-three solutions have been established.

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Cite This Study

Kulenović et al. (2025) studied this question.

synapsesocial.com/papers/68d45b3431b076d99fa5dfa2https://doi.org/10.3390/math13182990
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