| Title |
Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator–Prey System with the Allee Effect
|
|---|---|
| Published in |
Bulletin of Mathematical Biology, January 2018
|
| DOI | 10.1007/s11538-018-0394-6 |
| Pubmed ID | |
| Authors |
Maitri Verma, A. K. Misra |
| Abstract |
The extinction of species is a major threat to the biodiversity. The species exhibiting a strong Allee effect are vulnerable to extinction due to predation. The refuge used by species having a strong Allee effect may affect their predation and hence extinction risk. A mathematical study of such behavioral phenomenon may aid in management of many endangered species. However, a little attention has been paid in this direction. In this paper, we have studied the impact of a constant prey refuge on the dynamics of a ratio-dependent predator-prey system with strong Allee effect in prey growth. The stability analysis of the model has been carried out, and a comprehensive bifurcation analysis is presented. It is found that if prey refuge is less than the Allee threshold, the incorporation of prey refuge increases the threshold values of the predation rate and conversion efficiency at which unconditional extinction occurs. Moreover, if the prey refuge is greater than the Allee threshold, situation of unconditional extinction may not occur. It is found that at a critical value of prey refuge, which is greater than the Allee threshold but less than the carrying capacity of prey population, system undergoes cusp bifurcation and the rich spectrum of dynamics exhibited by the system disappears if the prey refuge is increased further. |
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| United States | 1 | 33% |
| Unknown | 2 | 67% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 2 | 67% |
| Scientists | 1 | 33% |
Mendeley readers
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 13 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 2 | 15% |
| Researcher | 2 | 15% |
| Student > Bachelor | 1 | 8% |
| Student > Master | 1 | 8% |
| Unknown | 7 | 54% |
| Readers by discipline | Count | As % |
|---|---|---|
| Mathematics | 3 | 23% |
| Environmental Science | 1 | 8% |
| Social Sciences | 1 | 8% |
| Engineering | 1 | 8% |
| Unknown | 7 | 54% |
Attention Score in Context
This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 11 April 2018.
All research outputs
#14,979,439
of 23,041,514 outputs
Outputs from Bulletin of Mathematical Biology
#682
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#256,118
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Outputs of similar age from Bulletin of Mathematical Biology
#20
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