scholarly journals Chaos in the Shimizu-Morioka Model With Fractional Order

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhangzhi Wei ◽  
Xin Zhang
Keyword(s):  
Fractional Calculus ◽  
Phase Diagrams ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Order Model ◽  
Dynamical Behaviors ◽  
Fractional Order Model

The investigation of dynamical behaviors for fractional-order chaotic systems is a new trend recently. This article is numerically concerned with the Shimizu-Morioka model with a fractional order. We find that chaos exists in the fractional-order model with order less than three by utilizing the fractional calculus techniques, and some phase diagrams are also constructed.

scholarly journals Modeling and Characteristics Analysis for a Buck-Boost Converter in Pseudo-Continuous Conduction Mode Based on Fractional Calculus

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Ningning Yang ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Boost Converter ◽  
Practical Significance ◽  
Order Model ◽  
Fractional Order Model ◽  
Conduction Mode ◽  
Continuous Conduction Mode

In recent days, fractional calculus (FC) has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the Buck-Boost converter in pseudo-continuous conduction mode (PCCM). Orders of the model are considered as extra parameters, and these parameters have significant influences on the performance of the model. The inductor current, the inductor current ripple, the amplitude of the output voltage, and the transfer functions of the fractional-order model are all related to orders. The contrast simulation experiments are conducted to investigate the performance of integer-order and fractional-order Buck-Boost converters in PCCM. Results of numerical and circuit simulations demonstrate that the proposed theoretical analysis is effective; the fractional-order model of the Buck-Boost converter in PCCM has certain theoretical and practical significance for modeling and performance analysis of other electrical or electronic equipment.

scholarly journals A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel

2021 ◽  
Vol 146 ◽  
pp. 110859
Author(s):  
Ahmed Boudaoui ◽  
Yacine El hadj Moussa ◽  
Zakia Hammouch ◽  
Saif Ullah
Keyword(s):  
Fractional Order ◽  
The Novel ◽  
Order Model ◽  
Fractional Order Model ◽  
Novel Coronavirus

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Permanent Magnet ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Synchronous Generator ◽  
Adaptive Controller ◽  
Control Technique ◽  
Order Model ◽  
Permanent Magnet Synchronous Generator ◽  
Chaos Suppression ◽  
Fractional Order Model

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

scholarly journals Identification of a PEMFC fractional order model

2017 ◽  
Vol 42 (2) ◽  
pp. 1499-1509 ◽  
Author(s):  
Miassa Amira Taleb ◽  
Olivier Béthoux ◽  
Emmanuel Godoy
Keyword(s):  
Fractional Order ◽  
Order Model ◽  
Fractional Order Model

A fractional-order model for MINMOD Millennium

2015 ◽  
Vol 262 ◽  
pp. 36-45 ◽  
Author(s):  
Yongjin Cho ◽  
Imbunm Kim ◽  
Dongwoo Sheen
Keyword(s):  
Fractional Order ◽  
Order Model ◽  
Fractional Order Model
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