# Stability analysis of prey predator model with Holling II functional response and threshold harvesting for the predator
> Yusrianto

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85074972349
Jurnal / Konferensi: Journal of Physics Conference Series
Tahun terbit: 2019
DOI: https://doi.org/10.1088/1742-6596/1341/6/062025
ISSN: 17426588
Citations: 12

## Authors
- Yusrianto

## Abstract
Abstract This paper deals with a prey predator model with Holling response function of type II and continuous threshold harvesting in the predator population. The prey grows as a logistic model when there is no interaction with the predator. The predator is assumed decreasing due to natural death and interspecific interaction when there is no interaction with its prey. The existence of the interior equilibrium point is considered and the stability is analysed using linearization and eigenvalues methods. The phase portrait of the model is also used to determine the behaviour of populations. From the analyses of the model with harvesting we found that there exists a stable interior equilibrium point. The predator population will remain sustainable when the size of the populations are initially close enough to the equilibrium point. But when the threshold value is too high and the populations are initially quite far from the equilibrium point, then the predator population may stop being harvested at a certain time. Some numerical simulations are given to confirm the result of analysis.

## Keywords
- Predator
- Equilibrium point
- Stability (learning theory)
- Functional response
- Population
- Mathematics
- Linearization
- Predation
- Applied mathematics
- Control theory (sociology)
- Ecology
- Mathematical analysis
- Biology
- Physics
- Nonlinear system
- Economics
- Computer science
- Differential equation
- Machine learning
- Control (management)
- Demography
- Sociology
- Quantum mechanics
- Management

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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