Dynamic behaviours and control of fractional-order memristor-based system

Pramana

Xiao Lv²  Yigang He³  Ranchao Wu¹  Liping Chen1³ 

[1] School of Mathematics, Anhui University, Hefei 230039, China$$;Chongqing Special Equipment Inspection and Research Institute, Chongqing 401121, China$$;School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China$$

关键词: Fractional order;    memristor circuit;    Hopf bifurcation;    chaos control.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Dynamics of fractional-order memristor circuit system and its control are investigated in this paper. With the help of stability theory of fractional-order systems, stability of its equilibrium points is analysed. Then, the chaotic behaviours are validated using phase portraits, the Lyapunov exponents and bifurcation diagrams with varying parameters. Furthermore, some conditions ensuring Hopf bifurcation with varying fractional orders and parameters are determined, respectively. By using a stabilization theorem proposed newly for a class of nonlinear systems, linear feedback controller is designed to stabilize the fractional-order system and the corresponding stabilization criterion is presented. Numerical simulations are given to illustrate and verify the effectiveness of our analysis results.

【 授权许可】

Unknown