THE ROLE OF RAPID DIFFUSION IN A SIMPLE FOOD CHAIN

1996 ◽  
Vol 04 (02) ◽  
pp. 249-259
Author(s):  
DEBASIS MUKHERJEE
Keyword(s):  
Steady State ◽  
Food Chain ◽  
Diffusion Coefficients ◽  
Local Stability ◽  
Threshold Value ◽  
Chain Model ◽  
Functional Responses ◽  
Stability And Instability ◽  
Food Chain Model

This paper deals with the stabilizing effect of diffusion on a four species food chain model. Conditions for local stability and instability of the model without diffusion are derived in terms of the threshold value of the functional responses of the predators at the steady state. It is also shown that an unstable equilibrium of the food chain without diffusion can be made stable for the model with diffusion, provided diffusion coefficients and predator functional responses satisfy certain threshold properties at the steady state. Lastly conditions for global stability of the model with diffusion are derived.

scholarly journals GLOBAL STABILITY OF A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND NONLOCAL DELAYS

2011 ◽  
Vol 16 (3) ◽  
pp. 376-389 ◽  
Author(s):  
Xiao Zhang ◽  
Rui Xu ◽  
Zhe Li
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Food Chain ◽  
Energy Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Chain Model ◽  
Food Chain Model ◽  
Theoretical Results

In this paper, a three species reaction-diffusion food-chain system with nonlocal delays is investigated. Sufficient conditions are derived for the global stability of a positive steady state and boundary steady states of the system by using the energy function method. Numerical simulations are carried out to illustrate the theoretical results.

The role of top predator interference on the dynamics of a food chain model

2013 ◽  
Vol 18 (3) ◽  
pp. 757-768 ◽  
Author(s):  
Ranjit Kumar Upadhyay ◽  
Raid Kamel Naji ◽  
Sharada Nandn Raw ◽  
Balram Dubey
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Top Predator ◽  
Predator Interference ◽  
Food Chain Model

scholarly journals Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses

2015 ◽  
Vol 20 (7) ◽  
pp. 2269-2290 ◽  
Author(s):  
Wen-Bin Yang ◽  
◽  
Yan-Ling Li ◽  
Jianhua Wu ◽  
Hai-Xia Li ◽  
...  
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Functional Responses ◽  
Ratio Dependent ◽  
Food Chain Model

Persistence and Stability of a Food Chain Model with Mixed Selection of Functional Responses

2006 ◽  
Vol 11 (2) ◽  
pp. 171-185 ◽  
Author(s):  
A. Maiti ◽  
B. Patra ◽  
G. P. Samanta
Keyword(s):  
Food Web ◽  
Functional Response ◽  
Food Chain ◽  
Building Blocks ◽  
Chain Model ◽  
Functional Responses ◽  
Interacting Species ◽  
Important Object ◽  
Food Chain Model ◽  
Selection Of

One approach to the study of an ecological community begins with an important object: its food web. Theoretical studies of food web must contend with the question of how to couple the large number of interacting species. One line of investigation assumes that the “building blocks” are species interacting in a pairwise fashion. The model we analyze in this paper describes a tritrophic food chain composed of logistic prey, a classical Lotka-Volterra functional response for prey and predator, and a Holling type-II functional response for predator and superpredator. Dynamical behaviours such as boundedness, stability, persistence, bifurcation et cetera of the model are studied critically. Computer simulations are carried out to explain the analytical findings. Finally it is discussed how these ideas illuminate some of the observed properties of real populations in the field, and explores practical implications.

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