scholarly journals Bifurcation Control of a Delayed Fractional Mosaic Disease Model for Jatropha curcas with Farming Awareness

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Shouzong Liu ◽  
Mingzhan Huang ◽  
Juan Wang
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Jatropha Curcas ◽  
Mosaic Disease ◽  
Bifurcation Control ◽  
Feedback Gain ◽  
Infection Model ◽  
Feedback Delay ◽  
Execution Delay ◽  
Farming Awareness

In this paper, the bifurcation control of a fractional-order mosaic virus infection model for Jatropha curcas with farming awareness and an execution delay is investigated. By analyzing the associated characteristic equation, Hopf bifurcation induced by the execution delay is studied for the uncontrolled system. Then, a time-delayed controller is introduced to control the occurrence of Hopf bifurcation. Our study implies that bifurcation dynamics is significantly affected by the change of the fractional order, the feedback gain and the extended feedback delay provided that the other parameters are fixed. A series of numerical simulations is performed, which not only verifies our theoretical results but also reveals some specific features. Numerically, we find that the Hopf bifurcation gradually occurs in advance with the increase of the fractional order, and there exist extreme points for the feedback gain and the extended feedback delay which can minimize the bifurcation value.

scholarly journals On the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji chaotic system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jianping Shi ◽  
Liyuan Ruan
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaotic System ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Delay Systems ◽  
Feedback Gain ◽  
Stability Of Equilibrium ◽  
Delayed Feedback Controller

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.

Stability and Bifurcation Control in a Fractional Predator–Prey Model via Extended Delay Feedback

2019 ◽  
Vol 29 (11) ◽  
pp. 1950150 ◽  
Author(s):  
Chengdai Huang ◽  
Huan Li ◽  
Tongxing Li ◽  
Shijun Chen
Keyword(s):  
Fractional Order ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Feedback Gain ◽  
Feedback Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Delayed Feedback Controller ◽  
Uncontrolled System

This paper explores the bifurcation control of a fractional predator–prey system with an active extended delayed feedback controller. Delay-induced bifurcations criteria for such an uncontrolled system are firstly derived by selecting time delay as a bifurcation parameter. Then, an extended delayed feedback controller is cleverly devised to control Hopf bifurcation for the proposed system. It means that the bifurcation dynamics can be efficaciously controlled for a given system with the adjustment of the fractional order, feedback gain and extended feedback delay provided that the remnant parameters are fixed. The obtained results significantly extend the preceding studies concerning bifurcation control of delayed fractional-order systems. To verify the correctness of the established theory, some numerical results are presented.

Impact of farming awareness and delay on the dynamics of mosaic disease in Jatropha curcas plantations

2018 ◽  
Vol 37 (5) ◽  
pp. 6108-6131 ◽  
Author(s):  
Fahad Al Basir ◽  
Ezio Venturino ◽  
Santanu Ray ◽  
Priti Kumar Roy
Keyword(s):  
Jatropha Curcas ◽  
Mosaic Disease ◽  
Farming Awareness

scholarly journals Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Shuai Li ◽  
Chengdai Huang ◽  
Xinyu Song
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Feedback Gain ◽  
Controlled System ◽  
Delay Feedback Control ◽  
Feedback Control Strategy ◽  
System With Time Delay ◽  
Theoretical Results ◽  
Predator System

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.

A fractional-order delay differential model for Ebola infection and CD8+ T-cells response: Stability analysis and Hopf bifurcation

2017 ◽  
Vol 10 (08) ◽  
pp. 1750111 ◽  
Author(s):  
V. Preethi Latha ◽  
Fathalla A. Rihan ◽  
R. Rakkiyappan ◽  
G. Velmurugan
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Ebola Virus ◽  
Cytotoxic T Lymphocyte ◽  
Response Term ◽  
Infection Model ◽  
Differential Model ◽  
Ctl Response

In this paper, we study a fractional-order model with time-delay to describe the dynamics of Ebola virus infection with cytotoxic T-lymphocyte (CTL) response in vivo. The time-delay is introduced in the CTL response term to represent time required to stimulate the immune system. Based on fractional Laplace transform, some conditions on stability and Hopf bifurcation are derived for the model. The analysis shows that the fractional-order with time-delay can effectively enrich the dynamics and strengthen the stability condition of fractional-order infection model. Finally, the derived theoretical results are justified by some numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document