Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization

doi:10.1088/1674-1056/24/8/080502

摘要/Abstract

摘要： A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points. In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.

关键词: fractional-order systems, equilibrium points, hyperchaotic systems, synchronization

Abstract: A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points. In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.

Key words: fractional-order systems, equilibrium points, hyperchaotic systems, synchronization

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.Xt (Synchronization; coupled oscillators)

Donato Cafagna, Giuseppe Grassi. Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization[J]. 中国物理B, 2015, 24(8): 80502-080502.

Donato Cafagna, Giuseppe Grassi. Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization[J]. Chin. Phys. B, 2015, 24(8): 80502-080502.

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