Nonlinear Dynamics

, Volume 95, Issue 3, pp 1841–1858 | Cite as

Dynamical behavior of a fractional three-species food chain model

  • J. AlidoustiEmail author
  • M. Mostafavi Ghahfarokhi
Original Paper


In this paper, a fractional three-species food chain model is considered. The boundedness of the solution of the fractional system has been proven. We analytically determine local and global stability and dynamical behaviors of the equilibria of this system. Further, condition under which a Hopf bifurcation may occur is derived. By using numerical analysis, we figure out that the model may have chaotic dynamics for realistic parameters. Transition to chaotic behavior is established via cycles, period-doubling bifurcation and period-halving bifurcation.


Bifurcation Stability analysis Caputo derivative Chaos Strange attractor Periodic solution 



This work is supported by the Shahrekord University of Iran under Grant Nos. 96PRM2M1192 and 96GRD1M1497. Compliance with ethical standards, the authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesShahrekord UniversityShahrekordIran
  2. 2.Department of Computer EngineeringShahrekord UniversityShahrekordIran

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