Nonlinear Dynamics

, 56:121

On stability, persistence, and Hopf bifurcation in fractional order dynamical systems

  • H. A. El-Saka
  • E. Ahmed
  • M. I. Shehata
  • A. M. A. El-Sayed
Original Paper

DOI: 10.1007/s11071-008-9383-x

Cite this article as:
El-Saka, H.A., Ahmed, E., Shehata, M.I. et al. Nonlinear Dyn (2009) 56: 121. doi:10.1007/s11071-008-9383-x

Abstract

This is a preliminary study about the bifurcation phenomenon in fractional order dynamical systems. Persistence of some continuous time fractional order differential equations is studied. A numerical example for Hopf-type bifurcation in a fractional order system is given, hence we propose a modification of the conditions of Hopf bifurcation. Local stability of some biologically motivated functional equations is investigated.

Keywords

Fractional orderBifurcation

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • H. A. El-Saka
    • 1
  • E. Ahmed
    • 2
  • M. I. Shehata
    • 2
  • A. M. A. El-Sayed
    • 3
  1. 1.Mathematics Department, Faculty of ScienceMansoura UniversityNew DamiettaEgypt
  2. 2.Mathematics Department, Faculty of ScienceMansoura UniversityMansouraEgypt
  3. 3.Mathematics Department, Faculty of ScienceAlexandria UniversityAlexandriaEgypt