TY - JOUR
T1 - Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay
AU - Pal, Nikhil
AU - Samanta, Sudip
AU - Biswas, Santanu
AU - Alquran, Marwan
AU - Al-Khaled, Kamel
AU - Chattopadhyay, Joydev
N1 - Funding Information:
Sudip Samanta’s research work is supported by Erasmus Mundus postdoctoral fellowship (EMINTE). Santanu Biswas’s research is supported by the Senior Research Fellowship from the University Grants Commission, Government of India. The research of J. Chattopadhyay is partially supported by a DST-SERB project (Ref No. SERB/F/0412/ 2013–2014).
Publisher Copyright:
© 2015 World Scientific Publishing Company.
PY - 2015/8/8
Y1 - 2015/8/8
N2 - 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.
AB - 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.
KW - Tri-trophic food chain
KW - bifurcation
KW - center manifold theorem
KW - chaos
KW - delay
KW - numerical simulation
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U2 - 10.1142/S0218127415501230
DO - 10.1142/S0218127415501230
M3 - Article
AN - SCOPUS:84940839121
SN - 0218-1274
VL - 25
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 9
M1 - 1550123
ER -