Bifurcation analysis of a food chain system incorporating time delay and the disease spreading among prey species

2018 ◽  
Author(s):  
Xinyou Meng ◽  
Nini Qin
Keyword(s):  
Time Delay ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Prey Species ◽  
Chain System ◽  
Disease Spreading

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay

2015 ◽  
Vol 25 (09) ◽  
pp. 1550123 ◽  
Author(s):  
Nikhil Pal ◽  
Sudip Samanta ◽  
Santanu Biswas ◽  
Marwan Alquran ◽  
Kamel Al-Khaled ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Period Doubling ◽  
Equilibrium Analysis ◽  
Chain Model ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Food Chain Model

In the present paper, we study the effect of gestation delay on a tri-trophic food chain model with Holling type-II functional response. The essential mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. Considering time-delay as the bifurcation parameter, the Hopf-bifurcation analysis is carried out around the coexisting equilibrium. The direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and center manifold theorem. We observe that if the magnitude of the delay is increased, the system loses stability and shows limit cycle oscillations through Hopf-bifurcation. The system also shows the chaotic dynamics via period-doubling bifurcation for further enhancement of time-delay. Our analytical findings are illustrated through numerical simulations.

Predator-dependent transmissible disease spreading in prey under Holling type-II functional response

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun K. Santra ◽  
Abdelalim A. Elsadany ◽  
Ghanshaym S. Mahapatra
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Linearization Method ◽  
Logistic Growth ◽  
Type Ii ◽  
Disease Spreading ◽  
Predator Interactions ◽  
The Stability ◽  
Infected Prey ◽  
Type Ii Functional Response

Abstract This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

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