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.

Details

Title
Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response
Author
Din, Qamar 1   VIAFID ORCID Logo  ; M Sajjad Shabbir 2 ; Khan, M Asif 1 ; Khalil, Ahmad 2 

1  Department of Mathematics, University of the Poonch Rawalakot, Rawalakot, Pakistan 
2  Department of Mathematics, Air University Islamabad, Islamabad, Pakistan 
End page
501
Publication year
2019
Publication date
Dec 2019
Publisher
Taylor & Francis Ltd.
ISSN
17513758
e-ISSN
17513766
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1080/17513758.2019.1638976
ProQuest document ID
2391993131
Copyright
© 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.