scholarly journals Chaotic Dynamics of the Fractional-Love Model with an External Force

2017 ◽  
Author(s):  
Linyun Huang ◽  
Youngchul Bae
Keyword(s):  
Nonlinear System ◽  
Periodic Function ◽  
Fractional Order ◽  
External Force ◽  
Chaotic Dynamics ◽  
Chaotic Dynamic ◽  
Fractional Order System ◽  
Order System ◽  
The Relationship ◽  
Fractional Orders

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.

Chaotic Dynamics of Fractional-Order Liu System

2011 ◽  
Vol 55-57 ◽  
pp. 1327-1331 ◽  
Author(s):  
Xin Gao
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Dynamics ◽  
Fractional Order System ◽  
Order System ◽  
Liu System

In this paper, we numerically investigate the chaotic behaviors of a new fractional-order system. We find that chaotic behaviors exist in the fractional-order system with order less than 3. The lowest order we find to have chaos is 2.4 in such system. In addition, we numerically simulate the continuances of the chaotic behaviors in the fractional-order system with orders from 2.7 to 3. Our investigations are validated through numerical simulations.

scholarly journals Coexisting Three-Scroll and Four-Scroll Chaotic Attractors in a Fractional-Order System by a Three-Scroll Integer-Order Memristive Chaotic System and Chaos Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xikui Hu ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Control ◽  
Initial Conditions ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Integer Order ◽  
Memristive System ◽  
Fractional Orders

Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with different initial conditions. Furthermore, we proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with different fractional-orders q. Meanwhile, with fractional-order q=0.965 and different initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. Finally, we discussed controlling chaos for the fractional-order memristive chaotic system.

scholarly journals Elegant Chaos in Fractional-Order System without Equilibria

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Donato Cafagna ◽  
Giuseppe Grassi
Keyword(s):  
Numerical Methods ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Dynamics ◽  
Fractional Order System ◽  
Order System ◽  
System Parameters ◽  
System Equations ◽  
Predictor Corrector

A new fractional-order chaotic system with no equilibria is presented. The proposed system can be considered elegant in the sense given by Sprott (2010), since the corresponding system equations contain very few terms and the system parameters have a minimum of digits. The chaotic dynamics are analyzed using the predictor-corrector algorithm when the fractional-order of the derivative is 0.98. Finally, the presence of chaos is validated by applying different numerical methods.

scholarly journals Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

2021 ◽  
Author(s):  
WANG Hongwei ◽  
ZHANG Qian ◽  
ZHA Qin ◽  
Mutalifu Ahemaide
Keyword(s):  
Fractional Order ◽  
Measurement Data ◽  
Estimation Algorithm ◽  
Fractional Order System ◽  
Order System ◽  
Identification Algorithm ◽  
Hammerstein System ◽  
Auxiliary Model ◽  
Marquardt Algorithm ◽  
Fractional Orders

Abstract Aiming at the modeling issues of fractional order Hammerstein system with scarce measurements, a novel multi-innovation hybrid identification algorithm is proposed to deal with them. Firstly, a multi-innovation estimation algorithm based on auxiliary model is presented to estimate the parameters of the nonlinear fractional order system, and a multi-innovation Levenberg-Marquardt algorithm are derived to confirm the fractional orders. Secondly, the convergence properties of the proposed algorithm are analyzed using the lemmas and theorems. Finally, in order to illustrate the effectiveness of the proposed algorithm, two fractional order nonlinear systems with scarce measurements are studied to prove the validity.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

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