On fractional-order symmetric oscillator with offset-boosting control
Articles
Changjin Xu
Guizhou University of Finance and Economics
https://orcid.org/0000-0001-5844-2985
Mati ur Rahman
Shanghai Jiao Tong University
https://orcid.org/0000-0002-4166-2006
Dumitru Baleanu
Cankaya University
Published 2022-07-19
https://doi.org/10.15388/namc.2022.27.28279
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Keywords

symmetric oscillator
Caputo operator
limit-cycle attractor
offset boosting

How to Cite

Xu C., Rahman M. ur and Baleanu D. (2022) “On fractional-order symmetric oscillator with offset-boosting control”, Nonlinear Analysis: Modelling and Control, 27(5), pp. 994-1008. doi: 10.15388/namc.2022.27.28279.

Abstract

This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and uniqueness of solutions for the suggested model are analyzed using the tools from fixed point theory. The symmetric oscillator is analyzed numerically and graphically with various fractional orders. It is observed that the fractional operator has a significant impact on the evolution of the oscillator dynamics showing that the system has a limit-cycle attractor. Offset-boosting control phenomena in the system are also studied with different orders and parameters.

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