Stability and Hopf bifurcation analysis in a three-level food chain system with delay

2007 ◽  
Vol 31 (3) ◽  
pp. 683-694 ◽  
Author(s):  
Yuanyuan Chen ◽  
Jiang Yu ◽  
Chengjun Sun
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Chain System ◽  
System With Delay

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.

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