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Stability, periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory
Author(s) -
GarićDemirović Mirela,
Nurkanović M.,
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.4000
Subject(s) - mathematics , homogeneous space , stability (learning theory) , order (exchange) , quadratic equation , mathematical physics , pure mathematics , mathematical analysis , geometry , finance , machine learning , computer science , economics
By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equationu n + 1 = A + B u n + u n 2( 1 + D u n ) u n − 1, n = 0 , 1 , 2 , …where A , B , D > 0, u −1 , u 0 >0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.