| Title | ON THE PERIODICITY OF LOZI’S EQUATION |
| Publication Type | Journal Article |
| Year of Publication | 2009 |
| Authors | M. RAGHIB, ABU-SARIS, K. NEDA’A, AL-JUBOURI |
| Secondary Title | Communications in Applied Analysis |
| Volume | 13 |
| Issue | 1 |
| Start Page | 47 |
| Pagination | 56 |
| Date Published | 01/2009 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 39A10, 39A20. |
| Abstract | We investigate the periodic nature of the solutions of the second order nonlinear difference equation
with real parameters, α, β, γ, and real initial condition, y−1 , y0 . Indeed, we show that if γ = 0, then all solutions are periodic of the same period p if and only if α = 0 and β = −1, in which case, p = 4. Also, we identify all periodic solutions of minimal period 2 and 3. |
| URL | http://www.acadsol.eu/en/articles/13/1/6.pdf |
| Short Title | PERIODICITY OF LOZI’S EQUATION |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] R. Abu-Saris, On the periodicity of the difference equation x n+1 = α|x n | + βx n−1 , Journal of Difference Equations and Applications 5 (1999), 57–69.
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[5] M. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations, Chapman & Hall / CRC, New York, 2002. [6] Z. Liu, H. Xie, Z. Zhu and Q. Lu, The strange attractor of Lozi mapping, International Journal of Bifurcation and Chaos 2 (1992), 831–839. [7] M. Misiurewicz, Strange attractors for the Lozi mapping, Nonlinear Dynamics, Annals of the New York Academy of Sciences 357 (1980), 348–358. |
