Stability, periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory | Zendy

GarićDemirović Mirela | Zendy; Nurkanović M. | Zendy; Nurkanović Z. | Zendy

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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.

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