Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions
Abstract Our investigation deals with the stability and permanence of diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions. Firstly, we prove that the solutions of this model are globally bounded and remain permanently in the positive...
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Online Access: | http://link.springer.com/article/10.1186/s13662-018-1621-z |
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doaj-d5057af04619459c80521c3ba9dd7a262020-11-25T01:41:37ZengSpringerOpenAdvances in Difference Equations1687-18472018-05-012018111710.1186/s13662-018-1621-zStability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensionsAka Fulgence Nindjin0Kessé Thiban Tia1Hypolithe Okou2Albin Tetchi3UFR de Mathématiques et Informatique, Université Félix Houphouët BoignyUFR de Mathématiques et Informatique, Université Félix Houphouët BoignyUFR de Mathématiques et Informatique, Université Félix Houphouët BoignyUFR de Mathématiques et Informatique, Université Félix Houphouët BoignyAbstract Our investigation deals with the stability and permanence of diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions. Firstly, we prove that the solutions of this model are globally bounded and remain permanently in the positive quadrant. From this system, we obtain three trivial equilibrium points of which, under certain conditions, one is locally stable and the others unstable. We show that the unique point of positive internal equilibrium is locally stable. Then, by constructing an appropriate Lyapunov’s functional, we establish the main result which is the global and asymptotic stability of this model. Finally, a numerical simulation is run to illustrate all these different theoretical results.http://link.springer.com/article/10.1186/s13662-018-1621-zHolling-2Leslie–GowerboundednesspermanenceLyapunov’s functionalequilibrium |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Aka Fulgence Nindjin Kessé Thiban Tia Hypolithe Okou Albin Tetchi |
spellingShingle |
Aka Fulgence Nindjin Kessé Thiban Tia Hypolithe Okou Albin Tetchi Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions Advances in Difference Equations Holling-2 Leslie–Gower boundedness permanence Lyapunov’s functional equilibrium |
author_facet |
Aka Fulgence Nindjin Kessé Thiban Tia Hypolithe Okou Albin Tetchi |
author_sort |
Aka Fulgence Nindjin |
title |
Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions |
title_short |
Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions |
title_full |
Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions |
title_fullStr |
Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions |
title_full_unstemmed |
Stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions |
title_sort |
stability of a diffusive predator–prey model with modified leslie–gower and holling-type ii schemes and time-delay in two dimensions |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2018-05-01 |
description |
Abstract Our investigation deals with the stability and permanence of diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions. Firstly, we prove that the solutions of this model are globally bounded and remain permanently in the positive quadrant. From this system, we obtain three trivial equilibrium points of which, under certain conditions, one is locally stable and the others unstable. We show that the unique point of positive internal equilibrium is locally stable. Then, by constructing an appropriate Lyapunov’s functional, we establish the main result which is the global and asymptotic stability of this model. Finally, a numerical simulation is run to illustrate all these different theoretical results. |
topic |
Holling-2 Leslie–Gower boundedness permanence Lyapunov’s functional equilibrium |
url |
http://link.springer.com/article/10.1186/s13662-018-1621-z |
work_keys_str_mv |
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