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Updated: Jan 22, 2026

Linking Predation Risk, Herbivore Physiological Stress and Microbial Decomposition of Plant Litter
Published on: March 12, 2013
Bifurcation analysis and chaos control for a plant-herbivore model with weak predator functional response
Qamar Din1, M Sajjad Shabbir2, M Asif Khan1
1a Department of Mathematics , University of the Poonch Rawalakot , Rawalakot , Pakistan.
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-herbivore 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-herbivore model undergoes Neimark-Sacker bifurcation. Numerical simulation is provided to strengthen our theoretical discussion.
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