带有三角函数的二维分数阶离散系统的混沌现象

doi:10.12066/j.issn.1007-2861.1934

上海大学学报(自然科学版) ›› 2019, Vol. 25 ›› Issue (2): 222-226.doi: 10.12066/j.issn.1007-2861.1934

带有三角函数的二维分数阶离散系统的混沌现象

刘明明¹, 夏铁成¹(), 王金波²

^1. 上海大学理学院, 上海 200444
^2. 中国电子科技集团公司第三十研究所国家保密通讯重点实验室,成都 610041

收稿日期:2017-05-22 出版日期:2019-04-30 发布日期:2019-05-05
通讯作者: 夏铁成 E-mail:xiatc@shu.edu.cn
基金资助:
国家自然科学基金资助项目(61072147, 11271108)

Two-dimensional fractional discrete chaos combined with trigonometric functions

LIU Mingming¹, XIA Tiecheng¹(), WANG Jinbo²

^1. College of Sciences, Shanghai University, Shanghai 200444, China
^2. Key Laboratory of Security Communications, The 30th Research Institute of China Electronics Technology Group Corporation,Chengdu 610041, China

Received:2017-05-22 Online:2019-04-30 Published:2019-05-05
Contact: Tiecheng XIA E-mail:xiatc@shu.edu.cn

摘要/Abstract

摘要：

推广一个带有三角函数的二维分数阶离散混沌系统到分数阶,并通过数值仿真得到不同分数阶差分下的分岔图、混沌解和相位图,以刻画分数阶时的混沌现象.

关键词: 分数阶差分, 分岔图, 混沌解, 相位图, 混沌现象

Abstract:

A discrete chaotic map combined with trigonometric functions is generalized to fractional ones. Through numerical simulation, the chaos behaviors of the maps are discussed by bifurcation diagrams,solutions and phase portraits when the difference orders are fractional.

Key words: fractional difference order, bifurcation diagram, chaotic solution, phase portraits, chaos behaviors

中图分类号:

O186.11

刘明明, 夏铁成, 王金波. 带有三角函数的二维分数阶离散系统的混沌现象[J]. 上海大学学报(自然科学版), 2019, 25(2): 222-226.

LIU Mingming, XIA Tiecheng, WANG Jinbo. Two-dimensional fractional discrete chaos combined with trigonometric functions[J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(2): 222-226.

图/表 5

参考文献 10

[1]	Atici F M, Eloe P W . A transform method in discrete fractional calculus[J]. International Journal of Difference Equations, 2007,2(2):165-176. doi: 10.1016/j.neunet.2019.11.004 pmid: 31785539
[2]	Atici F M, Eloe P W . Initial value problems in discrete fractional calculus[J]. Proceedings of the American Mathematical Society, 2009,137:981-989. doi: 10.1090/S0002-9939-08-09626-3
[3]	Atici F M, Sengul S . Modeling with fractional difference equations[J]. Journal of Mathematical Analysis and Applications, 2010,369(1):1-9. doi: 10.1186/s13058-019-1183-3 pmid: 31484577
[4]	Anastassiou G A . Nabla discrete fractional calculus and nabla inequalities[J]. Mathematical and Computer Modelling, 2010,51(5/6):562-571. doi: 10.1016/j.isatra.2018.12.016 pmid: 30578000
[5]	Abdeljawad T . On Riemann and Caputo fractional differences[J]. Computers and Mathematics with Applications, 2011,62(3):1602-1611. doi: 10.1016/j.camwa.2011.03.036
[6]	Abdeljawad T, Baleanu D . Fractional differences and integration by parts[J]. Journal of Computational Analysis and Applications, 2011,13(3):574-582.
[7]	Holm M T . The Laplace transform in discrete fractional calculus[J]. Computers and Mathematics with Applications, 2011,62(3):1591-1601. doi: 10.1016/j.camwa.2011.04.019
[8]	Li P, Min L, Hu Y, et al. Novel two dimensional discrete chaotic maps and simulations [C]//International Conference on Information and Automation for Sustainability. 2012: 159-162.
[9]	Wu G C, Baleanu D, Zeng S D . Discrete chaos in fractional sine and standard maps[J]. Physics Letters A, 2014,378(5/6):484-487. doi: 10.1016/j.physleta.2013.12.010
[10]	Goodrich C S . Existence of a positive solution to a system of discrete fractional boundary value problems[J]. Applied Mathematics and Computation, 2011,217(9):4740-4753. doi: 10.1016/j.amc.2010.11.029

带有三角函数的二维分数阶离散系统的混沌现象

Two-dimensional fractional discrete chaos combined with trigonometric functions

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