scholarly journals Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

2016 ◽  
Vol 4 (5) ◽  
pp. 59 ◽  
Author(s):  
Changyou Wang
Keyword(s):  
Feedback Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Globally Attractive

The Permanence of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

2013 ◽  
Vol 765-767 ◽  
pp. 327-330
Author(s):  
Chang You Wang ◽  
Xiang Wei Li ◽  
Hong Yuan
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Analysis Technique ◽  
Ratio Dependent

This paper is concerned with a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls. By developing a new analysis technique, we establish the sufficient conditions which guarantee the permanence of the model.

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.

scholarly journals Dynamics and bifurcations of a ratio-dependent predator-prey model

2022 ◽  
Vol 40 ◽  
pp. 1-20
Author(s):  
Parisa Azizi ◽  
Reza Khoshsiar Ghaziani
Keyword(s):  
Normal Form ◽  
Limit Cycles ◽  
Numerical Continuation ◽  
Predator Prey ◽  
Bifurcation Points ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating from a Hopf point.

Parametric analysis of the ratio-dependent predator-prey model

2001 ◽  
Vol 43 (3) ◽  
pp. 221-246 ◽  
Author(s):  
F. Berezovskaya ◽  
G. Karev ◽  
R. Arditi
Keyword(s):  
Parametric Analysis ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent
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