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Role of Induced Volatile Emission Modelling Tritrophic Interaction

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Abstract

Plant population response to herbivore attack by releasing volatile organic compounds (VOCs) in a highly regulated fashion. The natural enemies of herbivores are attracted by such induced volatile. This type of mechanism is known as “indirect defense mechanism” for plants. A tritrophic interaction among the plants, herbivores and their carnivorous enemies is considered along with “indirect defense mechanism” of plants in recruitment rate of carnivorous enemies. A systematic analysis of the dynamics of plant–herbivore–carnivore system with Holling type II functional response is done in this paper. The conditions for existence and feasibility of boundary and interior equilibrium points of the system are also determined. The conditions for the global stability of positive equilibrium point is derived. Persistence of the system is studied. Here, different types of bifurcations are analyzed with respect to many parameters. A key role is played by immigration rate of carnivores in determining the eventual state of the ecosystem. Finally, numerical simulations are performed to validate the obtained results.

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Acknowledgements

This research of Ritwika Mondal was supported by DST/INSPIRE Fellowship/ 2015/ IF 150747. The authors are grateful to the anonymous reviewers for their helpful comments in improving this paper.

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Authors and Affiliations

  1. Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, 700032, India

    Ritwika Mondal & Dipak Kesh

  2. Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata, 700063, India

    Debasis Mukherjee

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  1. Ritwika Mondal
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  2. Dipak Kesh
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  3. Debasis Mukherjee
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Correspondence to Dipak Kesh.

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Mondal, R., Kesh, D. & Mukherjee, D. Role of Induced Volatile Emission Modelling Tritrophic Interaction. Differ Equ Dyn Syst 30, 749–765 (2022). https://doi.org/10.1007/s12591-019-00458-y

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