Hopf-Type Bifurcation and Synchronization of a Fractional Order Van der Pol Oscillator
In this paper, the dynamical behaviors of an incommensurate fractional order Van der Pol oscillator are studied. First, based on the stability theory of fractional order systems, some sufficient conditions for the stability and Hpof-type bifurcation are given for such fractional order system. Then, the frequency and amplitude of periodic oscillations are determined by numerical simulations. It is shown that the frequency of oscillations gets smaller as the fractional order is increased, while the amplitude of oscillations increases with the fractional order. Finally, the synchronization of two coupled fractional order Van der Pol oscillators is analyzed with the help of the linear feedback control method. Numerical simulations are performed to verify the theoretical results.
Fractional order Van der Pol oscillator Hopf-type bifurcation Synchronization
XIAO Min ZHENG Wei Xing
School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 210017, P. School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith NSW 2751, Au
国际会议
The 31st Chinese Control Conference(第三十一届中国控制会议)
合肥
英文
193-198
2012-07-01（万方平台首次上网日期，不代表论文的发表时间）