Bifurcation analysis and chaos control of a second-order exponential difference equation
Keyword(s):
The aim of this article is to study the local stability of equilibria, investigation related to the parametric conditions for transcritical bifurcation, period-doubling bifurcation and Neimark-Sacker bifurcation of the following second-order difference equation xn+1 = ?xn + ?xn-1 exp(-?xn-1) where the initial conditions x-1, x0 are the arbitrary positive real numbers and ?,? and ? are positive constants. Moreover, chaos control method is implemented for controlling chaotic behavior under the influence of Neimark-Sacker bifurcation and period-doubling bifurcation. Numerical simulations are provided to show effectiveness of theoretical discussion.
2018 ◽
Vol 19
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pp. 53-68
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2014 ◽
Vol 2014
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pp. 1-13
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2012 ◽
Vol 22
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pp. 1250111
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2001 ◽
Vol 5
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pp. 315-325
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