scholarly journals On a three species ratio-dependent Lotka-Volterra cooperative system with delays

2021 ◽  
Vol 2021 (1) ◽  
Keyword(s):  
Cooperative System ◽  
Ratio Dependent

scholarly journals Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Azhar Halik ◽  
Hong-Li Li
Keyword(s):  
Time Delays ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Comparison Method ◽  
Cooperative System ◽  
Functional Responses ◽  
Feedback Controls ◽  
Lyapunov Function Method ◽  
Inequality Techniques ◽  
Ratio Dependent

AbstractThis study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical example is also presented to validate the practicability and feasibility of our proposed results.

Permanence and extinction analysis for a delayed ratio-dependent cooperative system with stage structure

2013 ◽  
Vol 25 (4) ◽  
pp. 897-909 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng ◽  
Xamxinur Abdurahman
Keyword(s):  
Stage Structure ◽  
Cooperative System ◽  
Ratio Dependent

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.

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