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摘要: 利用最近提出的广义分数阶微积分算子，研究了一类新的带Caputo型导数的广义分数阶混沌系统.讨论了混沌性质对导数阶数与系统参数的依赖性，利用有限差分法对广义分数阶混沌系统进行数值模拟，结果显示广义分数阶系统不仅蕴含经典混沌系统的结果，还展现出其他的动力学行为.由于广义分数阶混沌系统统一了多个不同的系统，未来该领域有望获得更进一步的研究.Abstract: In view of a new generalized fractional calculus proposed recently, this paper is devoted to applying the generalized fractional derivatives to study new generalized fractional chaotic systems. The chaotic properties depending on the new generalized fractional derivative are discussed and shown graphically. The generalized fractional derivative is described in the Caputo sense, and the finite difference approach for solving the generalized fractional chaotic system is presented. Since the generalized fractional derivative includes many existing fractional derivatives as special cases, we hope more attention will be brought into this field in the near future.
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Key words:
- Finite difference method /
- fractional calculus /
- fractional chaotic system /
- generalized fractional derivative /
- nonlinear dynamics
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Fig. 1 Phase portraits of GFLVS (top row, (a) and (b)) and GFLS (bottom row, (c) and (d)).
Fig. 2 Influence of scale function $\sigma(t)$ on GFLVS (top row, (a) and (b)) and GFLS (bottom row, (c) and (d)).
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