Global Stability for a Binary Reaction-Diffusion Lotka-Volterra Model with Ratio-Dependent Functional Response

2014 ◽  
Vol 132 (1) ◽  
pp. 151-163 ◽  
Author(s):  
Florinda Capone ◽  
Roberta De Luca
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Reaction Diffusion ◽  
Volterra Model ◽  
Ratio Dependent ◽  
Binary Reaction

scholarly journals Permanence of a Discrete Periodic Volterra Model with Mutual Interference

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Lijuan Chen ◽  
Liujuan Chen
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Volterra Model

This paper discusses a discrete periodic Volterra model with mutual interference and Holling II type functional response. Firstly, sufficient conditions are obtained for the permanence of the system. After that, we give an example to show the feasibility of our main results.

scholarly journals Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Wenzhen Gan ◽  
Canrong Tian ◽  
Qunying Zhang ◽  
Zhigui Lin
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Neumann Boundary Condition ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Food Ingestion ◽  
Nonlocal Delay ◽  
Homogeneous Neumann Boundary Condition

This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.

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