Chaos and Hopf bifurcation control in a fractional-order memristor-based chaotic system with time delay

2017 ◽  
Vol 132 (11) ◽  
Author(s):  
Dawei Ding ◽  
Xin Qian ◽  
Wei Hu ◽  
Nian Wang ◽  
Dong Liang
2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jianping Shi ◽  
Liyuan Ruan

Abstract In this paper, we study the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji (BG) chaotic system. Since the current study on Hopf bifurcation for fractional-order delay systems is carried out on the basis of analyses for stability of equilibrium of its linearized approximation system, it is necessary to verify the reasonability of linearized approximation. Through Laplace transformation, we first illustrate the equivalence of stability of equilibrium for a fractional-order delay Bhalekar–Gejji chaotic system and its linearized approximation system under an appropriate prior assumption. This semianalytically verifies the reasonability of linearized approximation from the viewpoint of stability. Then we theoretically explore the relationship between the time delay and Hopf bifurcation of such a system. By introducing the delayed feedback controller into the proposed system, the influence of the feedback gain changes on Hopf bifurcation is also investigated. The obtained results indicate that the stability domain can be effectively controlled by the proposed delayed feedback controller. Moreover, numerical simulations are made to verify the validity of the theoretical results.


Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Shuai Li ◽  
Chengdai Huang ◽  
Xinyu Song

The issue of bifurcation control for a novel fractional-order two-prey and one-predator system with time delay is dealt with in this paper. Firstly, the characteristic equation is investigated by picking time delay as the bifurcation parameter, and some conditions for the appearance of Hopf bifurcation are obtained. It is shown that time delay can give rise to periodic oscillations and each order has an important impact on the occurrence of Hopf bifurcation for the controlled system. Then, it is illustrated that the control result is obviously influenced by the feedback gain. It is also noted that the inception of the bifurcation can be postponed if the feedback gain decreases. Finally, two simulation examples are carried out to verify the chief theoretical results.


Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan

In this paper, we study a fractional order time delay for nonlinear financial system. By using Laplace transformation, stability and Hopf bifurcation analysis have been done for the model. Furthermore, numerical simulation has been carried out for better understanding of our results.


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