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Bifurcation and Chaos in Real Dynamics of a Two-Parameter Family Arising from Generating Function of Generalized Apostol-Type Polynomials

College of Engineering, Qassim University, Buraidah 52344, Saudi Arabia
Math. Comput. Appl. 2018, 23(1), 7; https://doi.org/10.3390/mca23010007
Received: 13 January 2018 / Revised: 30 January 2018 / Accepted: 1 February 2018 / Published: 3 February 2018
The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions f λ , n ( x ) = λ x ( e x + 1 ) n , λ > 0 , x R , n N \ { 1 } which arises from the generating function of the generalized Apostol-type polynomials. The existence of the real fixed points of f λ , n ( x ) and their stability are studied analytically and the periodic points of f λ , n ( x ) are computed numerically. The bifurcation diagrams and Lyapunov exponents are simulated; these demonstrate chaotic behaviour in the dynamical system of the function f λ , n ( x ) for certain ranges of parameter λ . View Full-Text
Keywords: real fixed points; periodic points; bifurcation; chaos; Lyapunov exponents real fixed points; periodic points; bifurcation; chaos; Lyapunov exponents
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Sajid, M. Bifurcation and Chaos in Real Dynamics of a Two-Parameter Family Arising from Generating Function of Generalized Apostol-Type Polynomials. Math. Comput. Appl. 2018, 23, 7.

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