Stability and Hopf Branch of Partial Profit
Model with Three Time Delays

SU Xiao-ya; ZHAI Yan-hui

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P511

Stability and Hopf Branch of Partial Profit Model with Three Time Delays

SU Xiao-ya, ZHAI Yan-hui

Citation :

SU Xiao-ya, ZHAI Yan-hui, "Stability and Hopf Branch of Partial Profit Model with Three Time Delays," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 79-98, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P511

Abstract

This paper mainly investigated a partial profit model with three discrete time delays. With two combinations of three time delays ζ1, ζ2, ζ as bifurcation parameters, we investigated the local stability of equilibrium point of the system and the sufficient condition for the existence of Hopf branch in two cases. Furthermore, we obtained the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions by using the center manifold theorem and normal form theory.At last, some numerical simulation results are confirmed that the feasibility of the theoretical analysis.

Keywords

partial profit model, stability,time delays ,center manifold theorem,Hopf bifurcation

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