带有三角函数的二维分数阶离散系统的混沌现象
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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.
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.
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.
引文
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[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.
[3]Atici F M,Sengul S.Modeling with fractional difference equations[J].Journal of Mathematical Analysis and Applications,2010,369(1):1-9.
[4]Anastassiou G A.Nabla discrete fractional calculus and nabla inequalities[J].Mathematical and Computer Modelling,2010,51(5/6):562-571.
[5]Abdeljawad T.On Riemann and Caputo fractional differences[J].Computers and Mathematics with Applications,2011,62(3):1602-1611.
[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.
[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.
[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.