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http://dx.doi.org/10.5666/KMJ.2020.60.2.401

Periodic Solutions of a System of Piecewise Linear Difference Equations  

Tikjha, Wirot (Faculty of Science and Technology, Pibulsongkram Rajabhat University)
Lapierre, Evelina (Department of Mathematics, Johnson and Wales University)
Publication Information
Kyungpook Mathematical Journal / v.60, no.2, 2020 , pp. 401-413 More about this Journal
Abstract
In this article we consider the following system of piecewise linear difference equations: xn+1 = |xn| - yn - 1 and yn+1 = xn + |yn| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.
Keywords
difference equation; periodic solution; stability;
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1 M. F. Barnsley, R. L. Devaney, B. B. Mandelbrot, H. O. Peitgen, D. Saupe, and R. F. Voss, The science of fractal images, Springer-Verlag, New York, 1988.
2 R. L. Devaney, A piecewise linear model of the the zones of instability of an area-preserving map, Phys. D, 10(1984), 387-393.   DOI
3 E. A. Grove and G. Ladas, Periodicities in nonlinear difference equations, Chapman Hall/CRC Press, New York, 2005.
4 E. A. Grove, E. Lapierre, and W. Tikjha, On the global behavior of $x_{n+1}={\left|x_n \right|}-y_n-1$and $y_{n+1}=x_n+{\left|y_n \right|}$, Cubo, 14(2012), 125-166.
5 E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci., 20(1963), 130-141.   DOI
6 R. Lozi, Un attracteur etrange du type attracteur de Henon, J. Phys., 39(1978), 9-10.   DOI
7 W. Tikjha and E. Lapierre, On the periodic behavior of a system of piecewise linear difference equations, Adv. Difference Equ. Discrete Dyn. Syst., 275-282, Springer Proc. Math. Stat. 212, 2017.
8 W. Tikjha, E. G. Lapierre, and Y. Lenbury, On the global character of the system of piecewise linear difference equations $x_{n+1}={\left|x_n \right|}-y_n-1$ and $y_{n+1}=x_n-{\left|y_n \right|}$, Adv. Difference Equ., (2010), Art. ID 573281, 14 pp.
9 W. Tikjha, E. G. Lapierre, and T. Sitthiwirattham, The stable equilibrium of a system of piecewise linear difference equations, Adv. Difference Equ., (2017), Paper NO. 67, 10 pp.