Periodic and Chaotic Orbits of a Discrete Rational System

被引：0
|
作者：
Lazaryan, N. [1 ]
Sedaghat, H. [1 ]
机构：
[1] Virginia Commonwealth Univ, Dept Math, Richmond, VA 23284 USA
来源：
DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2015年 / 2015卷
关键词：
SNAP-BACK REPELLERS; DIFFERENCE-EQUATIONS; PLANE MAPS; POPULATION-MODEL; QUADRATIC TERMS; GLOBAL DYNAMICS; FOCAL POINTS; DENOMINATOR; BEHAVIOR;
D O I：
10.1155/2015/519598
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study a rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system's parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the positive quadrant cannot be repelling and the system does not have a snap-back repeller. By folding the system into a second-order equation, we find special cases of the system with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within the positive quadrant of the plane.
引用
收藏
页数：8
相关论文
共 50 条
  • [31] Stabilization of unstable periodic orbits of chaotic maps
    Magnitskii, NA
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 34 (2-4) : 369 - 372
  • [32] Unstable periodic orbits and chaotic economic growth
    Ishiyama, K
    Saiki, Y
    CHAOS SOLITONS & FRACTALS, 2005, 26 (01) : 33 - 42
  • [33] Comment on "Optimal periodic orbits of chaotic systems"
    Zoldi, SM
    Greenside, HS
    PHYSICAL REVIEW LETTERS, 1998, 80 (08) : 1790 - 1790
  • [34] Stabilization of unstable periodic orbits of chaotic maps
    Magnitskii, N.A.
    Computers and Mathematics with Applications, 1997, 34 (2-4): : 369 - 372
  • [35] Complex periodic orbits and tunneling in chaotic potentials
    Creagh, SC
    Whelan, ND
    PHYSICAL REVIEW LETTERS, 1996, 77 (25) : 4975 - 4979
  • [36] On stabilization of unstable periodic orbits of chaotic maps
    Magnitskii, NA
    DOKLADY AKADEMII NAUK, 1997, 355 (06) : 747 - 749
  • [37] CHAOTIC AND PERIODIC MOTIONS OF SATELLITES IN ELLIPTIC ORBITS
    KOCH, BP
    BRUHN, B
    ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 1989, 44 (12): : 1155 - 1162
  • [38] Theory of the periodic orbits of a chaotic quantum well
    Narimanov, EE
    Stone, AD
    PHYSICAL REVIEW B, 1998, 57 (16) : 9807 - 9848
  • [39] Extended resonant feedback technique for controlling unstable periodic orbits of chaotic system
    Tamasevicius, Arunas
    Tamaseviciute, Elena
    Pyragiene, Tatjana
    Mykolaitis, Gytis
    Bumeliene, Skaidra
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (12) : 4273 - 4279
  • [40] Stabilizing Periodic Orbits of The Fractional Order Chaotic Van Der Pol System
    Rahimi, Mohammad A.
    Salarieh, Hasan
    Alasty, Aria
    PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION - 2010, VOL 8, PTS A AND B, 2012, : 175 - 183
12345