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

Huan Su; Wenxue Li; Xiaohua Ding

doi:10.1016/j.jmaa.2012.11.033

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

Huan Su^*
, Wenxue Li
, Xiaohua Ding

^*Corresponding author for this work

Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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∈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.

Original language	English
Pages (from-to)	25-34
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	400
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2012.11.033
State	Published - 1 Apr 2013
Externally published	Yes

Keywords

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

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10.1016/j.jmaa.2012.11.033

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abstract = "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∈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.",

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AU - Su, Huan

AU - Li, Wenxue

AU - Ding, Xiaohua

PY - 2013/4/1

Y1 - 2013/4/1

N2 - 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∈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.

AB - 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∈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.

KW - Hopf bifurcation

KW - Local stability

KW - Neimark-Sacker bifurcation

KW - Nonstandard finite difference methods

UR - https://www.scopus.com/pages/publications/84871695530

U2 - 10.1016/j.jmaa.2012.11.033

DO - 10.1016/j.jmaa.2012.11.033

M3 - 文章

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EP - 34

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

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

Abstract

Keywords

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