Diffusion-induced regular and chaotic patterns in a ratio-dependent predator–prey model with fear factor and prey refuge

2021 ◽  
Vol 31 (3) ◽  
pp. 033128
Author(s):  
Bhaskar Chakraborty ◽  
Hunki Baek ◽  
Nandadulal Bairagi
Keyword(s):  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

scholarly journals Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Lingshu Wang ◽  
Guanghui Feng
Keyword(s):  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Comparison Arguments ◽  
Ratio Dependent ◽  
Iteration Technique ◽  
Coexistence Equilibrium

A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, whenτ=τ0. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.

Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

2019 ◽  
Vol 29 (03) ◽  
pp. 1950036 ◽  
Author(s):  
R. Sivasamy ◽  
M. Sivakumar ◽  
K. Balachandran ◽  
K. Sathiyanathan
Keyword(s):  
Temporal Dynamics ◽  
Intake Rate ◽  
Diffusion Term ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting ◽  
Ratio Dependent ◽  
The Cross

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

Sign in / Sign up

Export Citation Format

Share Document