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On stability, persistence, and Hopf bifurcation in fractional order dynamical systems |
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| Authors: | H. A. El-Saka E. Ahmed M. I. Shehata A. M. A. El-Sayed |
| Affiliation: | 1. Mathematics Department, Faculty of Science, Mansoura University, New Damietta, Egypt 2. Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt 3. Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt |
| 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. |
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