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Power-law stability of Hausdorff derivative nonlinear dynamical systems
International Journal of Systems Science ( IF 4.3 ) Pub Date : 2020-03-11 , DOI: 10.1080/00207721.2020.1737262
D. L. Hu 1 , W. Chen 1 , H. G. Sun 1
Affiliation  

ABSTRACT The power law decay is widely observed in lab experiments and field observations. The Power-law stability, however, has little been reported in the literature. In this study, the definition of the Power-law stability is proposed, and then via the Lyapunov direct method, the Power-law stability of nonlinear dynamical systems based on the Hausdorff derivative is investigated. Furthermore, the fractal comparison principle is introduced to obtain the stability conditions for the dynamical systems of this type. Finally, two examples are given to elucidate the notion of Power-law stability.

中文翻译:

Hausdorff导数非线性动力系统的幂律稳定性

摘要 在实验室实验和现场观察中广泛观察到幂律衰减。然而,幂律稳定性在文献中鲜有报道。本研究首先提出幂律稳定性的定义,然后通过李雅普诺夫直接法研究了基于Hausdorff导数的非线性动力系统的幂律稳定性。此外,还引入了分形比较原理来获得该类型动力系统的稳定性条件。最后,给出两个例子来阐明幂律稳定性的概念。
更新日期:2020-03-11
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