scholarly journals Stability analysis of predator-prey models via the liapunov method

1977 ◽  
Vol 39 (3) ◽  
pp. 339-347 ◽  
Author(s):  
M GATTO ◽  
S RINALDI
Keyword(s):  
Stability Analysis ◽  
Predator Prey ◽  
Liapunov Method ◽  
Predator Prey Models

scholarly journals Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration

2019 ◽  
pp. 1-14
Author(s):  
Apima B. Samuel ◽  
Lawi O. George ◽  
Nthiiri J. Kagendo
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Food Source ◽  
Type Ii ◽  
Human Settlement ◽  
Natural Habitats ◽  
Predator Prey ◽  
Migration Rates ◽  
Predator Attack ◽  
Predator Prey Models

Predator-prey models describe the interaction between two species, the prey which serves as a food source to the predator. The migration of the prey for safety reasons after a predator attack and the predator in search of food, from a patch to another may not be instantaneous. In this paper, a Rosenzweig-MacAurther model with a Holling-type II predator functional response and time delay in the migration of both species is developed and analysed. Stability analysis of the system shows that depending on the prey growth and prey migration rates either both species go to extinction or co-exist. Numerical simulations show that a longer delay in the migration of the species leads makes the model to stabilize at a slower rate compared to when the delay is shorter. Relevant agencies likethe Kenya Wildlife Service should address factors that slow down migration of species, for example, destruction of natural habitats for human settlement and activities, which may cause delay in migration.

STABILITY ANALYSIS OF DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT DELAY

2006 ◽  
Vol 16 (02) ◽  
pp. 465-472 ◽  
Author(s):  
WEIHUA DENG ◽  
YUJIANG WU ◽  
CHANGPIN LI
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Finite Time ◽  
Time Dependent ◽  
Time Interval ◽  
Finite Time Interval ◽  
Predator Prey ◽  
Gauss Type ◽  
Predator Prey Models ◽  
The Stability

In this Letter, we study the stability of differential equations with time-dependent delay. Several theorems are established for stability on a finite time interval, called "interval stability" for simplicity, and Liapunov stability. These theorems are applied to the generalized Gauss-type predator–prey models, and satisfactory results are obtained.

Stability analysis of predator–prey models involving cross-diffusion

2019 ◽  
Vol 400 ◽  
pp. 132141 ◽  
Author(s):  
Jocirei D. Ferreira ◽  
Severino Horácio da Silva ◽  
V. Sree Hari Rao
Keyword(s):  
Stability Analysis ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Models
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