Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics

2019 ◽  
Vol 25 (11) ◽  
pp. 1568-1603 ◽  
Author(s):  
Azmy S. Ackleh ◽  
Md Istiaq Hossain ◽  
Amy Veprauskas ◽  
Aijun Zhang
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Evolutionary Dynamics ◽  
Predator Prey ◽  
Predator Prey Models

scholarly journals Stability analysis of an eco-epidemiological model incorporating a prey refuge

2010 ◽  
Vol 15 (4) ◽  
pp. 473-491 ◽  
Author(s):  
A. K. Pal ◽  
G. P. Samanta
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Computer Simulations ◽  
Discrete Time ◽  
Predator Population ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Discrete Time Delay ◽  
The Stability

The present paper deals with the problem of a predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, permanence, local and global stabilities are addressed. We have also studied the effect of discrete time delay on the model. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings.

Hydra effect and paradox of enrichment in discrete-time predator-prey models

2019 ◽  
Vol 310 ◽  
pp. 120-127 ◽  
Author(s):  
Vinicius Weide ◽  
Maria C. Varriale ◽  
Frank M. Hilker
Keyword(s):  
Discrete Time ◽  
Predator Prey ◽  
Paradox Of Enrichment ◽  
Hydra Effect ◽  
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.

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