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

Wei Liu & Yaolin Jiang

DOI: 10.4208/eajam.141214.050616a

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 differential-algebraic 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 = {Wei Liu and Yaolin Jiang}, 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 differential-algebraic 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 AU - Wei Liu & Yaolin Jiang 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 differential-algebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

Wei Liu and Yaolin Jiang. (2018). 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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