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

Nikhil Pal, Sudip Samanta, Santanu Biswas, Marwan Alquran, Kamel Al-Khaled, Joydev Chattopadhyay

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number1550123
JournalInternational Journal of Bifurcation and Chaos
Volume25
Issue number9
DOIs
Publication statusPublished - Aug 8 2015

Fingerprint

Food Chain Model
Hopf bifurcation
Bifurcation Analysis
Hopf Bifurcation
Stability Analysis
Time Delay
Time delay
Equilibrium Analysis
Center Manifold Theorem
Normal Form Theory
Period-doubling Bifurcation
Bifurcation (mathematics)
Functional Response
Bifurcation Theory
Chaotic Dynamics
System stability
Limit Cycle
Periodic Solution
Bifurcation
Enhancement

Keywords

  • bifurcation
  • center manifold theorem
  • chaos
  • delay
  • numerical simulation
  • Tri-trophic food chain

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

Cite this

Pal, N., Samanta, S., Biswas, S., Alquran, M., Al-Khaled, K., & Chattopadhyay, J. (2015). Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay. International Journal of Bifurcation and Chaos, 25(9), [1550123]. https://doi.org/10.1142/S0218127415501230

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay. / Pal, Nikhil; Samanta, Sudip; Biswas, Santanu; Alquran, Marwan; Al-Khaled, Kamel; Chattopadhyay, Joydev.

In: International Journal of Bifurcation and Chaos, Vol. 25, No. 9, 1550123, 08.08.2015.

Research output: Contribution to journalArticle

Pal, N, Samanta, S, Biswas, S, Alquran, M, Al-Khaled, K & Chattopadhyay, J 2015, 'Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay', International Journal of Bifurcation and Chaos, vol. 25, no. 9, 1550123. https://doi.org/10.1142/S0218127415501230
Pal, Nikhil ; Samanta, Sudip ; Biswas, Santanu ; Alquran, Marwan ; Al-Khaled, Kamel ; Chattopadhyay, Joydev. / Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay. In: International Journal of Bifurcation and Chaos. 2015 ; Vol. 25, No. 9.
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