Hopf Bifurcation Analysis for the van der Pol Equation with Discrete and Distributed Delays
نویسندگان
چکیده
We consider the van der Pol equation with discrete and distributed delays. Linear stability of this equation is investigated by analyzing the transcendental characteristic equation of its linearized equation. It is found that this equation undergoes a sequence of Hopf bifurcations by choosing the discrete time delay as a bifurcation parameter. In addition, the properties of Hopf bifurcation were analyzed in detail by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate and verify the theoretical analysis.
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SHAOWEN LI a,b , XIAOFENG LIAO a,c and SHAORONG LI a College of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, China; Department of Mathematics, Southwest University of Finance and Economics, Chengdu 610074, P. R. China; [email protected] Department of Computer Sciences and Engineering, Chongqing University, Chongqing 400044, P. R. China. [email protected]...
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