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thzotit ixhzvior in thx Rxzl KynzTits of z Onx azrzTxtxr FzTily of Funttions
PoAaPPad Pajid a and AbdullaA P. AlPuwaiyan b
aPxZAaniZal xnginxxring DxpartPxnt, Zollxgx of xnginxxring QaPPiP UnivxrPity, BuraidaA, QaPPiP, Paudi Arabia
bPxZAaniZal xnginxxring DxpartPxnt, UnayzaA Zollxgx of xnginxxring QaPPiP UnivxrPity, Paudi 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 = xR \ {1} is considered. The fixed points, periodic points and their nature are investigated for the function . Bifurcation is shown to occur in the dynamics of . Period doubling, which is a route of chaos in the real dynamics, is also shown to take place in the real dynamics of . The orbits of the dynamics of are graphically represented by time series graphs. Moreover, the chaotic behavior in the dynamics of is found by computing positive Lyapunov exponents.
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Keywords: Bifurcation; chaos; dynamics; fixed point; Lyapunov exponents.
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©
2014
CSME , ISSN 0257-9731
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