Stability And Hopf Branch of A Predator-prey Model with Two Time Delays And Refuges Effect

SU Xiao-ya; ZHAIYan-hui

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P503

Stability And Hopf Branch of A Predator-prey Model with Two Time Delays And Refuges Effect

SU Xiao-ya, ZHAIYan-hui

Citation :

SU Xiao-ya, ZHAIYan-hui, "Stability And Hopf Branch of A Predator-prey Model with Two Time Delays And Refuges Effect," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 12-31, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P503

Abstract

This paper mainly investigated a Predator-prey Model with two time delays and refuges effect .By analyzing the characteristic equations, we discussed the local stability of equilibrium point of the system and the sufficient condition for the existence of Hopf branch. By choosing the delay as a bifurcation parameter,we can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions by using the centermanifold theorem and normal form theory. At last, some numerical simulation results are confirmed that the feasibility of the theoretical analysis.

Keywords

Hopf bifurcation,Stability,Two time delays ,Center manifold theorem,Predator-prey Model

References

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