Period-doubling bifurcations in the family of Chebyshev-Halley-type methods

被引：5

作者：

Cordero, Alicia ^{[1
]}

Torregrosa, Juan R. ^{[1
]}

Vindel, P. ^{[2
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46071 Valencia, Spain

[2] Univ Jaume 1, Inst Matemat & Aplicac Castellon, Castellon de La Plana, Spain

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2013年 / 90卷 / 10期

关键词：

numerical methods; Chebyshev-Halley methods; bifurcations; dynamics of numerical method; period-doubling bifurcation; 37F10; 37G15; ITERATIVE METHODS; DYNAMICS;

D O I：

10.1080/00207160.2012.745518

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The choice of a member of a parametric family of iterative methods is not always easy. The family of Chebyshev-Halley schemes is a good example of it. The analysis of bifurcation points of this family allows us to define a real interval in which there exist several problematic behaviours: attracting points that become doubled, other ones that become periodic orbits, etc. These aspects should be avoided in an iterative procedure, so it is important to determine the regions where this conduct takes place. In this paper, we obtain that this family admits attractive 2-cycles in two different intervals, for real values of the parameter.

引用

页码：2061 / 2071

页数：11

共 38 条

[11] Small-signal amplification of period-doubling bifurcations in smooth iterated maps [J].

Zhao, Xiaopeng ;

Schaeffer, David G. ;

Berger, Carolyn M. ;

Gauthier, Daniel J. .

NONLINEAR DYNAMICS, 2007, 48 (04) :381-389

[12] Period-doubling bifurcations for systems of difference equations and applications to models in population biology [J].

Selgrade, JF ;

Roberds, JH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 29 (02) :185-199

[13] Small-signal amplification of period-doubling bifurcations in smooth iterated maps [J].

Xiaopeng Zhao ;

David G. Schaeffer ;

Carolyn M. Berger ;

Daniel J. Gauthier .

Nonlinear Dynamics, 2007, 48 :381-389

[14] Period-doubling and Neimark-Sacker bifurcations in a larch budmoth population model [J].

De Silva, T. Mihiri M. ;

Jang, Sophia R. -J. .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2017, 23 (10) :1619-1639

[15] Orbits of period two in the family of a multipoint variant of Chebyshev-Halley family [J].

Beatriz Campos ;

Alicia Cordero ;

Juan R. Torregrosa ;

Pura Vindel .

Numerical Algorithms, 2016, 73 :141-156

[16] The distinct stochastic and deterministic dynamics between period-adding and period-doubling bifurcations of neural bursting patterns [J].

Yuye Li ;

Huaguang Gu .

Nonlinear Dynamics, 2017, 87 :2541-2562

[17] The distinct stochastic and deterministic dynamics between period-adding and period-doubling bifurcations of neural bursting patterns [J].

Li, Yuye ;

Gu, Huaguang .

NONLINEAR DYNAMICS, 2017, 87 (04) :2541-2562

[18] SYNCHRONY-BREAKING PERIOD-DOUBLING BIFURCATIONS FOR THREE-CELL HOMOGENEOUS COUPLED MAPS [J].

Comanici, Adela .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2009, 19 (04) :1157-1167

[19] Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems [J].

Berns, DW ;

Moiola, JL ;

Chen, GR .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1998, 45 (07) :759-763

[20] An efficient family of Chebyshev–Halley’s methods for system of nonlinear equations [J].

Ramandeep Behl .

Journal of Mathematical Chemistry, 2020, 58 :868-885

← 1 2 3 4 →