International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12
line decor
  
line decor

 Volume 7, Issue 5 (May 2020), Pages: 98-103

----------------------------------------------

 Original Research Paper

 Title: Dynamical properties of a 2-D non-invertible system

 Author(s): M. Mammeri *

 Affiliation(s):

 Department of Mathematics, Kasdi Merbah University, Ouargla, Algeria

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-2960-4214

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.05.012

 Abstract:

The non-invertible systems are very useful in practical applications. The study of the non-invertible systems has important value since a large number of genetics studies in biology, physics, engineering, and economic systems have been widely carried out found to exhibit a class of non-invertible systems. This short paper proposes a new simple four-term 2-D polynomial chaotic system with only one quadratic nonlinearity and describes its some interesting dynamical properties. Moreover, the stability of the fixed point and chaotic motions are investigated using analytical and numerical methods. Our 2-D polynomial system displays new chaotic attractors via the quasi-periodic route to chaos for certain values of its parameter of bifurcation. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Non-invertible 2-D map, Properties, Open connected subset, Quasi-periodic route to chaos

 Article History: Received 30 September 2019, Received in revised form 20 February 2020, Accepted 20 February 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Mammeri M (2020). Dynamical properties of a 2-D non-invertible system. International Journal of Advanced and Applied Sciences, 7(5): 98-103

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2

 Tables

 No Table

----------------------------------------------

 References (16) 

  1. Aziz-Alaoui MA, Robert C, and Grebogi C (2001). Dynamics of a Hénon–Lozi-type map. Chaos, Solitons and Fractals, 12(12): 2323-2341. https://doi.org/10.1016/S0960-0779(00)00192-2   [Google Scholar]
  2. Benedicks M and Carleson L (1991). The dynamics of the Hénon map. Annals of Mathematics, 133(1): 73-169. https://doi.org/10.2307/2944326   [Google Scholar]
  3. Benerjee S and Verghese GC (2001). Nonlinear phenomena in power electronics, attractor, bifurcations. IEEE Press, Piscataway, USA. https://doi.org/10.1109/9780470545393   [Google Scholar]
  4. Bi P and Ruan S (2013). Bifurcations in delay differential equations and applications to tumor and immune system interaction models. SIAM Journal on Applied Dynamical Systems, 12(4): 1847-1888. https://doi.org/10.1137/120887898   [Google Scholar]
  5. Bischi GI and Tramontana F (2010). Three-dimensional discrete-time Lotka–Volterra models with an application to industrial clusters. Communications in Nonlinear Science and Numerical Simulation, 15(10): 3000-3014. https://doi.org/10.1016/j.cnsns.2009.10.021   [Google Scholar]
  6. Cao Y and Liu Z (1998). Strange attractors in the orientation-preserving Lozi map. Chaos Solitons and Fractals, 9(11): 1857-1864. https://doi.org/10.1016/S0960-0779(97)00180-X   [Google Scholar]
  7. Elaydi S (1996). An introduction to difference equations. Springer, Berlin, Germany.  https://doi.org/10.1007/978-1-4757-9168-6   [Google Scholar]
  8. Gałach M (2003). Dynamics of the tumor-immune system competition-the effect of time delay. International Journal of Applied Mathematics and Computer Science, 13: 395-406.   [Google Scholar]
  9. Hénon M (1969). Numerical study of quadratic area-preserving mappings. Quarterly of Applied Mathematics, 27(3): 291-312. https://doi.org/10.1090/qam/253513   [Google Scholar]
  10. Hénon M (1976). A two-dimensional mapping with a strange at-tractor. Communications in Mathematical Physics, 50(1): 69-77. https://doi.org/10.1007/BF01608556   [Google Scholar]
  11. Mammeri M (2017). A unified behavior of 2-D and 3-D noninvertible map. International Journal of Pure and Applied Mathematics, 114(3): 611-618.   [Google Scholar]
  12. Mammeri M (2018). A trivial dynamics in 2-D square root discrete mapping. Applied Mathematical Sciences, 12(8): 363-368. https://doi.org/10.12988/ams.2018.8121   [Google Scholar]
  13. Marotto FR (1979). Chaotic behavior in the Hénon mapping. Communications in Mathematical Physics, 68(2): 187-194. https://doi.org/10.1007/BF01418128   [Google Scholar]
  14. Miller DA and Grassi G (2001). A discrete generalized hyperchaotic Hénon map circuit. In the 44th IEEE 2001 Midwest Symposium on Circuits and Systems, IEEE, Dayton, USA, 1: 328-331. https://doi.org/10.1109/MWSCAS.2001.986179   [Google Scholar]
  15. Tse TK (2003). Complex behavior of switching power converters. CRC Press, Boca Raton, USA. https://doi.org/10.1201/9780203494554   [Google Scholar]
  16. Zeraoulia E and Sprott JC (2010). 2-D quadratic maps and 3-D ODE systems: A rigorous approach. World Scientific, Singapore, Singapore. https://doi.org/10.1142/7774   [Google Scholar]