Volume 6, Issue 4
Dynamics of a Modified Predator-Prey System to allow for a Functional Response and Time Delay

Wei Liu & Yaolin Jiang

East Asian J. Appl. Math., 6 (2016), pp. 384-399.

Published online: 2018-02

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  • Abstract

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

  • Keywords

Predator-prey system, harvesting, stability, time delay, periodic solutions.

  • AMS Subject Headings

92D25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-384, author = {}, title = {Dynamics of a Modified Predator-Prey System to allow for a Functional Response and Time Delay}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {4}, pages = {384--399}, abstract = {

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.141214.050616a}, url = {http://global-sci.org/intro/article_detail/eajam/10806.html} }
TY - JOUR T1 - Dynamics of a Modified Predator-Prey System to allow for a Functional Response and Time Delay JO - East Asian Journal on Applied Mathematics VL - 4 SP - 384 EP - 399 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.141214.050616a UR - https://global-sci.org/intro/article_detail/eajam/10806.html KW - Predator-prey system, harvesting, stability, time delay, periodic solutions. AB -

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

Wei Liu & Yaolin Jiang. (2020). Dynamics of a Modified Predator-Prey System to allow for a Functional Response and Time Delay. East Asian Journal on Applied Mathematics. 6 (4). 384-399. doi:10.4208/eajam.141214.050616a
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