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

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.