The Dynamical Properties of Modified of Bogdanov Map

Authors

  • Wafaa H. Al-Hilli Department of Mathematics, College of Education University of AL-Qadisiyah
  • Rehab Amer Kamel Department of Mathematics, College of Education for pure Sciences, University of Babylon,Iraq

DOI:

https://doi.org/10.29304/jqcm.2021.13.2.790

Keywords:

Sensitive dependence on initial conditions, Lyapunov exponent, Topological entropy

Abstract

In the work, we study the general properties of  modified of the Bogdanov map in the form  Fa,m,k .

q.jpg

        We prove it  has sensitive dependence  on initial conditions and positive  Lyapunov exponent with some conditions . So we give estimate of topological entropy of modified Bogdanov map .

Downloads

Download data is not yet available.

References

Gulick D., ”Encounters with Chaos”, McGraw-Hill, Inc., New York,1992.

Katok S. R., "The Estimation from above for the Topological Entropy of a Diffeomorphism. Global Theory of Dynamical Systems", Lect. Notes Math. 819, pp. 258–264, 1980.

Rasolk. A. H., "On Henon map", College of Education University of Bablyon, January, 2006.

Bogdanov, R.I., "Bifurcation of the limit cycle of a family of plane vector fields" , Trudy Sem. Petrovsk. 2, 23. In Russian: the English translation is Sel. Math. Sov. Vol.1, No.4, PP.373-88,1981.

Simonsen Jakob Grue.," On The Computability of The Topological, Discrete Mathematics and Theoretical Computer Science", Vol.8, (2006), pp83-96.

Vicente Aboites &etal.,"Bogdanov map for Modelling a phase- conjugated Ring Resonator",vol.21(4),pp384.

Mohsin Al-juboori, A. (2017). A novel Approach to improve biometric authentication using Steerable-Locality Sensitive Discriminant Analysis. Journal of Al-Qadisiyah for Computer Science and Mathematics, 9(1), 61-70. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/16.

Jabbar Kadhim, I., & Kadhim Jebur, S. (2017). Study of Some Dynamical Concepts in General Topological spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 9(1), 12-22. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/9.

Arif, G., Wuhaib, S., & Rashad, M. (2020). Infected Intermediate Predator and Harvest in Food Chain. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Math Page 120 -. https://doi.org/10.29304/jqcm.2020.12.1.683.

Gaze Salih Al-Khafajy, D., & Abdulridha Mutar, M. (2017). On DM- Compact Smarandache Topological Semigroups. Journal of Al-Qadisiyah for Computer Science and Mathematics, 8(2), 25-33. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/30.

Mahdy Ali, S. (2017). Redefine Fuzzy Topological Vector Space by using Michalek’s Fuzzy Topological Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 7(2), 61-65. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/64.

AL-Taï‚¢aiiA., A.AL-Mayahi, N., & Youssif Hussein, B. (2017). On Equivalent Martingale Measures on Lp-space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 2(1), 6-13. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/207.

Abdul khalik Alkhafaji, M., & Himza Almyaly, A. (2017). Countability Axioms in Smooth Fuzzy Topological Spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 7(1), 41-52. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/85.

MAHDI ALI, S. (2017). A new kind of Fuzzy Topological Vector Spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 3(2), 63-72. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/275.

Downloads

Published

2021-05-07

How to Cite

Al-Hilli, W. H., & Kamel, R. A. (2021). The Dynamical Properties of Modified of Bogdanov Map. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(2), Math Page 14– 21. https://doi.org/10.29304/jqcm.2021.13.2.790

Issue

Section

Math Articles