Numerical Hopf bifurcation of linear multistep methods for a class of delay differential equations

作者：Liu M Z^*; Wang Qiubao

来源：Applied Mathematics and Computation, 2009, 208(2): 462-474.

DOI：10.1016/j.amc.2008.12.013

• Delay differential equations
• The strictly stable linear multistep method
• Hopf bifurcation

In this paper, we consider the discretization of parameter-dependent delay differential equation of the form
y'(t) = f(y(t), y(t - 1), tau), tau >= 0, y is an element of R(d).
It is shown that if the delay differential equation undergoes a Hopf bifurcation at tau = tau*, then the discrete scheme undergoes a Hopf bifurcation at tau(h) = tau* O(h(p)) for sufficiently small step size h, where p >= 1 is the order of the strictly stable linear multistep method. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of the corresponding delay differential equation.

• 出版日期2009-2-15
• 单位哈尔滨工业大学