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

Mustafa R. S. Kulenović () and Ryan Sullivan
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Mustafa R. S. Kulenović: Department of Mathematics, University of Rhode Island, Kingston, RI 02881, USA
Ryan Sullivan: Department of Mathematics, University of Rhode Island, Kingston, RI 02881, USA

Mathematics, 2025, vol. 13, issue 18, 1-14

Abstract: The third-order difference equation y n + 1 = a 1 y n 2 1 + y n 2 + a 2 y n − 1 2 1 + y n − 1 2 + a 3 y n − 2 2 1 + y n − 2 2 , 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.

Keywords: basin; difference equation; equilibrium; global stability; monotonicity; periodic solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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