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ISSN 2063-5346
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A delayed plant-herbivore model with a strong Allee effect in plant population

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Pankaj Kumar1; Rupali Verma2*
» doi: 10.48047/ecb/2023.12.10.014

Abstract

The article accommodates a delayed plant-herbivore model consolidating the strong Allee effect with intraspecific competition among herbivores. The Holling type- functional response is utilized which describes that an individual predator consumes food till it feels famished. The time delay is also considered in the model due to which the equilibrium losses stability. The associated state variables are: plant population and herbivore population. The non-trivial equilibrium point is calculated for the strong Allee effect. It is observed that the system is stable about the non-trivial equilibrium. The observation of Hopf- bifurcation is shown at the crucial value of the time delay. Moreover, it is found that the entire system becomes more and more stable while the intraspecific competition rate of herbivores keeps on increasing as represented in time series graphs. The analytical results are shown graphically with the help of MATLAB software to illustrate the proposed mathematical model.The article accommodates a delayed plant-herbivore model consolidating the strong Allee effect with intraspecific competition among herbivores. The Holling type- functional response is utilized which describes that an individual predator consumes food till it feels famished. The time delay is also considered in the model due to which the equilibrium losses stability. The associated state variables are: plant population and herbivore population. The non-trivial equilibrium point is calculated for the strong Allee effect. It is observed that the system is stable about the non-trivial equilibrium. The observation of Hopf- bifurcation is shown at the crucial value of the time delay. Moreover, it is found that the entire system becomes more and more stable while the intraspecific competition rate of herbivores keeps on increasing as represented in time series graphs. The analytical results are shown graphically with the help of MATLAB software to illustrate the proposed mathematical model.

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