EQUILIBRIUM POINT AND PERIODIC WITH PERIOD 5 OF A SYSTEM OF DIFFERENCE EQUATIONS

  • Wirot Tikjha
  • Pratya Phatson
Keywords: Difference equation, Equilibrium point, Periodic solution

Abstract

In this paper we study a two-dimensional piecewise linear system of difference equations. Initial conditions are negative x axis. We found a unique equilibrium point and two 5 cycles in the system. We separate the axis into intervals and we used direct calculations and single inductive statement in each interval of the axis to describe all behaviors in each interval of initial condition. Behaviors of solution to the system depend on choosing initial condition. It is either eventually equilibrium point or eventually prime period 5. This results could extent to understand global behaviors of family in piecewise linear system of difference equations.

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References

Cannings C, Hoppensteadt FC, Segel LA. Epidemic Modelling: An Introduction, New York, NY: Cambridge University Press; 2005.
Cull P. Difference Equations as Bilogical Models. Scientiae Mathematicae Japonicae e-2006: 965-981.
Devanney RL. A piecewise linear model of the the zones of instability of an area-preservingmap. Physica. 1984; 10D: 387-393.
Grove EA, Ladas G. Periodicities in Nonlinear Difference Equations. New York, NY: Chapman Hall; 2005.
Grove EA, Lapierre E, Tikjha W. On the Global Behavior of and . Cubo Mathematical Journal. 2012; 14: 125–166.
Krinket S, Tikjha W. Prime period solution of cartain piecewise linear system of
difference equation. Proceedings of the Pibulsongkram Research: 2015: 76-83.
Lozi R. Un attracteur etrange du type attracteur de Henon. Journal de Physique, Colloque. 1978; 39: 9-10.
Tikjha W, Lenbury Y, Lapierre EG, On the Global Character of the System of Piecewise Linear Difference Equations and . Advances in Difference Equations. 2010; Article ID 573281 (14 pages), doi:10.1155/2010/573281(2010).
Tikjha W, Lapierre EG, Sitthiwirattham T. The stable equilibrium of a system of piecewise linear difference equations. Advances in Difference Equations. 2017; 67 (10 pages), doi: 10.1186/s13662-017-1117-2(2017).
Published
2020-05-08
How to Cite
Tikjha, W., & Phatson, P. (2020). EQUILIBRIUM POINT AND PERIODIC WITH PERIOD 5 OF A SYSTEM OF DIFFERENCE EQUATIONS . Life Sciences and Environment Journal, 21(1), 1-12. Retrieved from https://ph01.tci-thaijo.org/index.php/psru/article/view/209562
Section
Research Articles