%0 Journal Article
%T Bifurcation analysis and chaos control for a plant¨Cherbivore model with weak predator functional response
%A Khalil Ahmad
%A M. Asif Khan
%A M. Sajjad Shabbir
%A Qamar Din
%J Journal of Biological Dynamics
%D 2019
%R https://doi.org/10.1080/17513758.2019.1638976
%X Abstract The interaction between plants and herbivores is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of plants and herbivores interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the interaction of the apple twig borer and the grape vine, the qualitative behaviour of a discrete-time plant¨Cherbivore model is investigated with weak predator functional response. The topological classification of equilibria is investigated. It is proved that the boundary equilibrium undergoes transcritical bifurcation, whereas unique positive steady-state of discrete-time plant¨Cherbivore model undergoes Neimark¨CSacker bifurcation. Numerical simulation is provided to strengthen our theoretical discussion
%U https://www.tandfonline.com/doi/full/10.1080/17513758.2019.1638976