Call for Paper - January 2024 Edition
IJCA solicits original research papers for the January 2024 Edition. Last date of manuscript submission is December 20, 2023. Read More

Applications of Bifurcation and Chaos on Discrete Time Dynamical System

Print
PDF
 
Download Full Text
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 162 - Number 6
Year of Publication: 2017
Authors:
Sharmin Akter, Asia Khatun
10.5120/ijca2017913320

Sharmin Akter and Asia Khatun. Applications of Bifurcation and Chaos on Discrete Time Dynamical System. International Journal of Computer Applications 162(6):1-6, March 2017. BibTeX

@article{10.5120/ijca2017913320,
	author = {Sharmin Akter and Asia Khatun},
	title = {Applications of Bifurcation and Chaos on Discrete Time Dynamical System},
	journal = {International Journal of Computer Applications},
	issue_date = {March 2017},
	volume = {162},
	number = {6},
	month = {Mar},
	year = {2017},
	issn = {0975-8887},
	pages = {1-6},
	numpages = {6},
	url = {http://www.ijcaonline.org/archives/volume162/number6/27244-2017913320},
	doi = {10.5120/ijca2017913320},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

In this paper the study of rigorous basic dynamical facts on bifurcation and chaos for discrete models in time dynamics and introduce a generalized logistic map and its dynamical behavior with tent and Henon Map has recognized.Different discrete curves have been developed and more general biological logistic curve are studied. Review and compare several such maps and analysis properties of those maps on the applications of bifurcation and chaos. Discuss the concept of chaos and bifurcations in the discrete time dynamical tent maps and generalized logistic growth models as time dynamical attractor.

References

  1. Devaney, R.L., A First Course in Chaotic Dynamical Systems, Perseus Press, 1993.
  2. Devaney, R.L., an Introduction to Chaotic Dynamical Systems, Westview Press, 2003.
  3. Holmgren R.A, A First Course in Discrete Dynamical Systems, spring-verlag, 1996.
  4. Robert M. May, Simple Mathematical Models with very Complicated Dynamics, Nature 261, 459-467, 1976.
  5. M. Martelli, On the Definition of Chaos.
  6. Wiley-Interscience, Introduction to Discrete Dynamical Systems and Chaos, 1999.
  7. Li, T.-y., and Yorke J., Period Three Implies Chaos. American Mathematical Monthly 82 (1975), 985-992.
  8. L. Chuang, Rice University Lectures, http://math.rice.edu/ lukec/teaching/FA-05/MATH211/budworm.pdf

Keywords

Chaos, Bifurcations, Logistic Map, Tent Map, Henon Map, Periodic points, constant, chaotic behavior.