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Coexistence of multiple attractors for an incommensurate fractional-order chaotic system

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Abstract

In this paper, a new 4-D incommensurate fractional-order chaotic system based on adomian decomposition method is investigated. The equilibrium points of the system with incommensurate orders are analyzed. The coexisting attractors of the system with different parameters and orders are unveiled through coexisting attractors phase diagram, coexisting bifurcation model, coexisting Lyapunov exponent spectrum. The effects of the incommensurate orders of the system are also analyzed. Meanwhile, some special phenomena such as hidden attractors and chaos degradation are found. The results show that the new 4-D incommensurate fractional-order chaotic system has rich dynamic characteristics. In addition, using the DSP platform to realize the system, the results are in good agreement with those on simulation. The research results provide a theoretical basis for the application of incommensurate order chaotic systems in secure communication.

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Acknowledgements

This work was supported by the Basic Scientific Research Projects of Colleges and Universities of Liaoning Province (Grant nos. 2017J045); Provincial Natural Science Foundation of Liaoning (Grant nos. 20170540060); National Nature Science Foundation of China (no. 61773010).

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Correspondence to Jun Mou.

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Ma, C., Mou, J., Liu, J. et al. Coexistence of multiple attractors for an incommensurate fractional-order chaotic system. Eur. Phys. J. Plus 135, 95 (2020). https://doi.org/10.1140/epjp/s13360-019-00093-0

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