East Asian J. Appl. Math., 9 (2019), pp. 122-152.
Published online: 2019-01
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A predator-prey system with Holling type II functional response and a time lag is described by a delayed differential-algebra system and the local asymptotic stability and Hopf bifurcation of such system is studied. It is shown that if the time lag increases, a sequence of Hopf bifurcations can occur. The stability and direction of the Hopf bifurcations are studied by using center manifold theory for functional differential equations. A numerical example illustrates our theoretical findings.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070318.070518}, url = {http://global-sci.org/intro/article_detail/eajam/12938.html} }A predator-prey system with Holling type II functional response and a time lag is described by a delayed differential-algebra system and the local asymptotic stability and Hopf bifurcation of such system is studied. It is shown that if the time lag increases, a sequence of Hopf bifurcations can occur. The stability and direction of the Hopf bifurcations are studied by using center manifold theory for functional differential equations. A numerical example illustrates our theoretical findings.