International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Mohammad Sajida* and Abdullah S. Alsuwaiyanb

aMechanical Engineering Department, College of Engineering Qassim University, Buraidah, Qassim, Saudi Arabia
bMechanical Engineering Department, Unayzah College of Engineering Qassim University, Saudi Arabia


 

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ABSTRACT


The chaotic behavior in the real dynamics of a one parameter family of nonlinear functions is studied in the present paper. For this purpose, the function   fλ (x) = λ· xex /( x 1 λ> 0, x ∈ \  {1}  is  considered.  The  fixed  points,  periodic  points  and  their  nature  are investigated for the function fλ (x).  Bifurcation is shown to occur in the dynamics of fλ (x). Period doubling, which is a route of chaos in the real dynamics, is also shown to take place in the real dynamics of fλ (x). The orbits of the dynamics of  fλ (x) are graphically represented by time series graphs. Moreover, the chaotic behavior in the dynamics of computing positive Lyapunov exponents.


Keywords: Bifurcation; chaos; dynamics; fixed point; Lyapunov exponents.


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ARTICLE INFORMATION


Received: 2013-11-23
Revised: 2014-06-11
Accepted: 2014-07-09
Available Online: 2014-12-01


Cite this article:

Sajid, M., Alsuwaiyan, A.S. 2014. Chaotic behavior in the real dynamics of a one parameter family of functions. International Journal of Applied Science and Engineering, 12, 289–301. https://doi.org/10.6703/IJASE.2014.12(4).289