Bifurcation analysis and chaos control for a plant-herbivore model with weak predator functional response

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 i...

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Bibliographic Details
Published in:Journal of biological dynamics 2019-01, Vol.13 (1), p.481-501
Main Authors: Din, Qamar, Shabbir, M. Sajjad, Khan, M. Asif, Ahmad, Khalil
Format: Article
Language:English
Subjects:
Borers
chaos control
Herbivores
Mathematical models
Neimark-Sacker bifurcation
Plant-herbivore model
stability
transcritical bifurcation
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Summary: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.
ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2019.1638976