Fractional-order delayed predator–prey systems with Holling type-II functional response

F. A. Rihan, S. Lakshmanan, A. H. Hashish, R. Rakkiyappan, E. Ahmed

Research output: Contribution to journalArticlepeer-review

148 Citations (Scopus)


In this paper, a fractional dynamical system of predator–prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order (Formula presented). It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model.

Original languageEnglish
Pages (from-to)777-789
Number of pages13
JournalNonlinear Dynamics
Issue number1-2
Publication statusPublished - Apr 2015


  • Fractional calculus
  • Hopf bifurcation
  • Predator–prey
  • Stability
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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