Impulsive Effect on Tri-Trophic Food Chain Model with Mixed Functional Responses under Seasonal Perturbations

2016 ◽  
Vol 26 (1-3) ◽  
pp. 157-176 ◽  
Author(s):  
Chandrima Banerjee ◽  
Pritha Das
Keyword(s):  
Food Chain ◽  
Impulsive Effect ◽  
Chain Model ◽  
Functional Responses ◽  
Food Chain Model

Rich dynamics of a food chain model with Hassell–Varley type functional responses

2009 ◽  
Vol 208 (2) ◽  
pp. 303-317 ◽  
Author(s):  
Sweta Pathak ◽  
Alakes Maiti ◽  
G.P. Samanta
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Functional Responses ◽  
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

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.

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.

scholarly journals Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III

2016 ◽  
Vol 39 (14) ◽  
pp. 3996-4006 ◽  
Author(s):  
Gamaliel Blé ◽  
Víctor Castellanos ◽  
Jaume Llibre
Keyword(s):  
Food Chain ◽  
Limit Cycles ◽  
Chain Model ◽  
Type Ii ◽  
Functional Responses ◽  
Food Chain Model

scholarly journals Effect of Time-Delay on a Ratio-Dependent Food Chain Model

2009 ◽  
Vol 14 (2) ◽  
pp. 199-216 ◽  
Author(s):  
B. Patra ◽  
A. Maiti ◽  
G. P. Samanta
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Food Chain ◽  
Chain Model ◽  
Functional Responses ◽  
Simple Criterion ◽  
Delayed System ◽  
Ratio Dependent ◽  
Food Chain Model ◽  
Practical Implications

This paper aims to study the effect of time-delay on a tritrophic food chainmodel with Michaelis-Menten type ratio-dependent functional responses. Boundednessof the time-delayed system is established. A simple criterion for deterministic extinctionis derived. It has been shown that the time-delay may introduce instability in the systemthrough Hopf bifurcation. Computer simulations are carried out to explain the analyticalfindings. It is discussed how these ideas illuminate some of the observed properties ofreal populations in the field, and explores practical implications.

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