Hopf bifurcation analysis in a predator–prey model with time delay and food subsidies View Full Text


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Article Info

DATE

2019-12

AUTHORS

Yuxiao Guo, Nannan Ji, Ben Niu

ABSTRACT

We analyze the stability of positive equilibrium in a predator-prey model with time delay τ and subsidies. The sufficient conditions of the local Hopf bifurcations at the positive equilibrium are obtained. By center manifold theorem and normal form theory, we analyze the direction of Hopf bifurcations and stability of the bifurcating periodic solution. Using the global Hopf bifurcation theorem, we find that each connected component is unbounded. High-dimensional Bendixson theorem is used to prove that the system has no nonconstant periodic solutions of τ-period, then we obtain the global existence of periodic solutions. Finally, a numerical example is performed to support the theoretical results, and the effect of the food subsidy is discussed. We find that the food subsidy will make the stable interval [0,τ0) of positive equilibrium larger with τ0 the first Hopf bifurcation value. More... »

PAGES

99

Journal

TITLE

Advances in Difference Equations

ISSUE

1

VOLUME

2019

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13662-019-2050-3

DOI

http://dx.doi.org/10.1186/s13662-019-2050-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112646039


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