Numerical dynamics of a nonstandard finite difference method for a class of delay differential equations

作者：Su, Huan^*; Li, Wenxue; Ding, Xiaohua

来源：Journal of Mathematical Analysis and Applications, 2013, 400(1): 25-34.

DOI：10.1016/j.jmaa.2012.11.033

• Nonstandard finite difference methods
• Local stability
• Hopf bifurcation
• Neimark-Sacker bifurcation

This paper proposes a nonstandard finite difference (NSFD) method for a class of delay differential equations. We prove that, for any step size h = 1/m (m is an element of Z(+)), this numerical method could intrinsically preserve the qualitative behavior of the dynamical system, including the local stability of equilibrium, the existence and the direction of Hopf bifurcation and the stability of bifurcating periodic solution. Finally, to illustrate the analytic results, the NSFD method is used for a model of the survival of red blood cells in animals.

• 出版日期2013-4-1
• 单位哈尔滨工业大学