Multiple bifurcation analysis in a NDDE arising from van der Pol's equation with extended delay feedback

作者：Niu, Ben; Jiang, Weihua^*

来源：Nonlinear Analysis: Real World Applications , 2013, 14(1): 699-717.

DOI：10.1016/j.nonrwa.2012.07.028

• Neutral equation
• Codimension two bifurcation
• Periodic solution
• Extended delay feedback
• Van der Pol's equation

Van der Pot's equation with extended delay feedback control is considered, which is equivalent to a system of neutral differential-difference equations (NDDEs). Fold bifurcation and Hopf bifurcation in this NDDE are studied by the formal adjoint theory, the center manifold theorem and the normal form method. These methods are also first employed in studying the Bogdanov-Takens singularity of NDDE. Bifurcation sets theoretically indicate the existence of a homoclinic orbit and the coexistence of three periodic solutions, which are all illustrated by the numerical methods. The coexistence of three stable periodic solutions and the existence of stable torus near the Hopf-fold and Hopf-Hopf bifurcations are also illustrated, respectively.

• 出版日期2013-2
• 单位哈尔滨工业大学; 哈尔滨学院