Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems
Xianggang Liu and
Li Ma
Applied Mathematics and Computation, 2020, vol. 385, issue C
Abstract:
The main intention of this paper is to investigate the dynamics of fractional Cubic map and fractional Holmes map from four perspectives: chaos, bifurcation, stabilization and synchronization. Via Jacobian matrix algorithm, we estimate the largest Lyapunov exponents of fractional maps to examine the existence of chaos in accordance with the observation of chaotic vibration affected by fractional difference order. In addition, with the help of the novel asymptotic stability criterion for linear incommensurate fractional difference systems, the effective control laws of stabilization and synchronization for fractional chaotic maps are achieved, respectively. Besides, experimental investigations and numerical simulations are implemented to further verify the effectiveness of the proposed results.
Keywords: Discrete fractional calculus; Chaotic vibration; Bifurcation; Stabilization; Synchronization (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (2)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320303842
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303842
DOI: 10.1016/j.amc.2020.125423
Access Statistics for this article
Applied Mathematics and Computation is currently edited by Theodore Simos
More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu (repec@elsevier.com).