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One-to-four-wing hyperchaotic fractional-order system and its circuit realization

机译：一到四翼超声分数阶系统及其电路实现

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PurposeThis paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems with variable-wing attractors, although some chaotic systems can generate one-to-four-wing attractors, none of them are hyperchaotic attractors, which is incomplete for the dynamic characteristics of chaotic systems.Design/methodology/approachA novel 4D fractional-order hyperchaotic system is proposed based on the classical three-dimensional Lu system. The complex and abundant dynamic behaviors of the fractional-order system are analyzed by phase diagrams, bifurcation diagrams and the corresponding Lyapunov exponents. In addition, SE and C-0 algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of order q on the system is also investigated. Finally, the circuit is implemented using physical components.FindingsThe most particular interest is that the system can generate one-to-four-wing hyperchaotic attractors with only one parameter variation. Then, the hardware circuit experimental results tally with the numerical simulations, which proves the validity and feasibility of the fractional-order hyperchaotic system. Besides, under different initial conditions, coexisting attractors can be obtained by changing the parameter d or the order q. Then, the complexity analysis of the system shows that the fractional-order chaotic system has higher complexity than the corresponding integer-order chaotic system.Originality/valueThe circuit structure of the fractional-order hyperchaotic system is simple and easy to implement, and one-to-four-wing hyperchaotic attractors can be observed in the circuit. To the best of the knowledge, this unique phenomenon has not been reported in any literature. It is of great reference value to analysis and circuit realization of fractional-order chaotic systems.
机译：目的纸张旨在介绍一种新型4D超色度分数阶系统，可以生产一对四翼超声吸引子。在研究具有可变翼吸引子的混沌系统中，虽然一些混沌系统可以产生一对四翼的吸引子，但它们都不是超鲜吸引子，这对于混沌系统的动态特征是不完整的.design/methodology/approacha基于经典三维LU系统提出了新的4D分数阶超声系统。分数顺序系统的复杂和丰富的动态行为被相图，分叉图和相应的Lyapunov指数分析。此外，SE和C-0算法用于分析分数级系统的复杂性。然后，还研究了订单Q对系统的影响。最后，电路使用物理组件实现.Findingsthe最特别的兴趣是系统可以产生一到四翼超声吸引子，只有一个参数变化。然后，硬件电路实验结果与数值模拟进行计数，这证明了分数阶超声系统的有效性和可行性。此外，在不同的初始条件下，可以通过改变参数d或订单q来获得共存吸引子。然后，系统的复杂性分析表明，分数阶混沌系统具有比相应整数混沌系统更高的复杂性。分数级超声系统的viglinity / valsete电路结构简单且易于实现，并且易于实现在电路中可以观察到四翼超声吸引子。据知识中，任何文献都没有报告这种独特的现象。分析和电路实现分数秩序混沌系统是很大的参考价值。

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