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Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation
Author(s) -
Kulenović M. R. S.,
Moranjkić S.,
Nurkanović Z.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3722
Subject(s) - mathematics , attractor , sigmoid function , bifurcation , pure mathematics , mathematical analysis , nonlinear system , physics , quantum mechanics , machine learning , artificial neural network , computer science
T. Wanner We investigate global dynamics of the equationx n + 1 =x n − 1 2b x nx n − 1 + c x n − 1 2 + f ,n = 0 , 1 , 2 , … ,where the parameters b , c , and f are nonnegative numbers with condition b + c > 0, f ≠ 0 and the initial conditions x −1 , x 0 are arbitrary nonnegative numbers such that x −1 + x 0 >0. We obtain precise characterization of basins of attraction of all attractors of this equation and describe the dynamics in terms of bifurcations of period‐two solutions. Copyright © 2015 John Wiley & Sons, Ltd.