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Volume 9, Issue 1
Bifurcation in a Differential-Algebra Predator-Prey System with Time Lag Effects

Wei Liu & Yaolin Jiang

East Asian J. Appl. Math., 9 (2019), pp. 122-152.

Published online: 2019-01

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  • Abstract

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.

  • AMS Subject Headings

92D25

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-122, author = {Wei Liu and Yaolin Jiang}, title = {Bifurcation in a Differential-Algebra Predator-Prey System with Time Lag Effects}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {122--152}, abstract = {

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} }
TY - JOUR T1 - Bifurcation in a Differential-Algebra Predator-Prey System with Time Lag Effects AU - Wei Liu & Yaolin Jiang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 122 EP - 152 PY - 2019 DA - 2019/01 SN - 9 DO - http://doi.org/10.4208/eajam.070318.070518 UR - https://global-sci.org/intro/article_detail/eajam/12938.html KW - Predator-prey, bifurcation, time lag, parametrisation, harvesting. AB -

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.

Wei Liu and Yaolin Jiang. (2019). Bifurcation in a Differential-Algebra Predator-Prey System with Time Lag Effects. East Asian Journal on Applied Mathematics. 9 (1). 122-152. doi:10.4208/eajam.070318.070518
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