Bifurcation analysis of modified Leslie-Gower predator-prey model with double Allee effect
| Autor: | Manoj Kumar Singh, Brajesh Kumar Singh, Beer S. Bhadauria |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Population
Saddle-node bifurcation Bifurcation diagram 01 natural sciences symbols.namesake Control theory Predator-prey system Applied mathematics Quantitative Biology::Populations and Evolution Homoclinic orbit 0101 mathematics education Bifurcation Mathematics Allee effect Hopf bifurcation education.field_of_study 010102 general mathematics General Engineering Engineering (General). Civil engineering (General) Biological applications of bifurcation theory 010101 applied mathematics Double Allee effect symbols TA1-2040 Stability |
| Zdroj: | Ain Shams Engineering Journal, Vol 9, Iss 4, Pp 1263-1277 (2018) |
| ISSN: | 2090-4479 |
| Popis: | In the present article, a modified Leslie-Gower predator-prey model with double Allee effect, affecting the prey population, is proposed and analyzed. We have considered both strong and weak Allee effects separately. The equilibrium points of the system and their local stability have been studied. It is shown that the dynamics of the system are highly dependent upon the initial conditions. The local bifurcations (Hopf, saddle-node, Bogdanov-Takens) have been investigated by considering sufficient parameter(s) as the bifurcation parameter(s). The local existence of the limit cycle emerging through Hopf bifurcation and its stability is studied by means of the first Lyapunov coefficient. The numerical simulations have been done in support of the analytical findings. The result shows the emergence of homoclinic loop. The possible phase portraits and parametric diagrams have been depicted. Keywords: Predator-prey system, Stability, Bifurcation, Double Allee effect |
| Databáze: | OpenAIRE |
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