Coexistence of attractors in autonomous Van der Pol–Duffing jerk oscillator: Analysis, chaos control and synchronisation in its fractional-order form

Pramana ◽  
2018 ◽  
Vol 91 (1) ◽  
Author(s):  
Victor Kamdoum Tamba ◽  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Hilaire Bertrand Fotsin ◽  
Pierre Kisito Talla
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Van Der Pol ◽  
Order Form ◽  
Coexistence Of Attractors

Three-dimensional chaotic autonomous van der pol–duffing type oscillator and its fractional-order form

2018 ◽  
Vol 56 (5) ◽  
pp. 2560-2573 ◽  
Author(s):  
Gaetan Fautso Kuiate ◽  
Sifeu Takougang Kingni ◽  
Victor Kamdoum Tamba ◽  
Pierre Kisito Talla
Keyword(s):  
Fractional Order ◽  
Three Dimensional ◽  
Van Der Pol ◽  
Order Form

Analysis of fractional order Bonhoeffer–van der Pol oscillator

2008 ◽  
Vol 387 (2-3) ◽  
pp. 418-424 ◽  
Author(s):  
V. Gafiychuk ◽  
B. Datsko ◽  
V. Meleshko
Keyword(s):  
Fractional Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Analytical solutions of nonlinear system of fractional-order Van der Pol equations

2018 ◽  
Vol 95 (4) ◽  
pp. 2837-2854 ◽  
Author(s):  
Shankar Rao Munjam ◽  
Rajeswari Seshadri
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Van Der Pol ◽  
Van Der Pol Equations

scholarly journals Study of fractional order Van der Pol equation

2016 ◽  
Vol 28 (1) ◽  
pp. 55-60 ◽  
Author(s):  
V. Mishra ◽  
S. Das ◽  
H. Jafari ◽  
S.H. Ong
Keyword(s):  
Fractional Order ◽  
Van Der Pol Equation ◽  
Van Der Pol
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