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

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.

scholarly journals Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1244
Author(s):  
Maria Francesca Carfora ◽  
Isabella Torcicollo
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Fear Effect ◽  
Group Defense ◽  
The Cross ◽  
The Stability

In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document