Bifurcation Analysis of Logistic Map Using Four Step Feedback Procedure
Sudesh Kumari1, Renu Chugh2, Ashish Nandal3
1Sudesh Kumari*, Department of Mathematics, Government College, Gurugram, India.
2Renu Chugh, Department of Mathematics, Maharshi Dayanand University, Rohtak, India.
3Ashish Nandal, Department of Mathematics, Pt. NRS Government College, Rohtak, India.
Manuscript received on September 15, 2019. | Revised Manuscript received on October 05, 2019. | Manuscript published on October 30, 2019. | PP: 704-707 | Volume-9 Issue-1, October 2019 | Retrieval Number: F9166088619/2019©BEIESP | DOI: 10.35940/ijeat.F9166.109119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The logistic map occupies a renowned place in the dynamics of chaos theory and in diverse areas of science. Picard orbit and Superior orbit (Mann orbit) have been used to control this discrete chaotic dynamical system. In this article, we further extend the analytical study of logistic map using a four step feedback procedure (SP orbit). The dynamical properties such as fixed point, range of convergence and stability, periodicity and chaos of the logistic map have been investigated. These properties are illustrated experimentally by adopting dynamical techniques like fixed point analysis and bifurcation plot. Using this approach, one can easily control the chaotic system and make the system stable for higher values of population growth parameter r by selecting the control parameters carefully.
Keywords: Bifurcation plot, Dynamical system, Fixed point, Four step feedback procedure, Logistic map.