Bifurcation control of a fractional-order delayed competition and cooperation model of two enterprises

2019 ◽  
Vol 62 (12) ◽  
pp. 2130-2143 ◽  
Author(s):  
ChangJin Xu ◽  
MaoXin Liao ◽  
PeiLuan Li
Keyword(s):  
Fractional Order ◽  
Bifurcation Control ◽  
Competition And Cooperation ◽  
Cooperation Model

scholarly journals NEW INSIGHTS ON BIFURCATION IN A FRACTIONAL-ORDER DELAYED COMPETITION AND COOPERATION MODEL OF TWO ENTERPRISES

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Changjin Xu ◽  
◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Shuai Yuan ◽  
...  
Keyword(s):  
Fractional Order ◽  
Competition And Cooperation ◽  
Cooperation Model

scholarly journals Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 970 ◽  
Author(s):  
Rohisha Tuladhar ◽  
Fidel Santamaria ◽  
Ivanka Stamova
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Impulsive Control ◽  
Control Strategies ◽  
Volterra Type ◽  
Stability Behavior ◽  
Integer Order ◽  
Order Case ◽  
Cooperation Model ◽  
Stability Results

We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n−species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.

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.

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