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

Mathematical and Computational Applications

Sajid, Mohammad¹ 

关键词: real fixed points;    periodic points;    bifurcation;    chaos;    Lyapunov exponents;   

DOI  :  10.3390/mca23010007

学科分类：计算数学

来源: mdpi

【 摘 要 】

The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functionsfλ , n( x )= λx (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 offλ , n( x )and their stability are studied analytically and the periodic points offλ , n( x )are computed numerically. The bifurcation diagrams and Lyapunov exponents are simulated; these demonstrate chaotic behaviour in the dynamical system of the functionfλ , n( x )for certain ranges of parameterλ .

【 授权许可】

CC BY