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 differential-algebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.