A novel chaotification scheme for fractional system and its application

Little seems to be known about the chaotification control of fractional order linear and nonlinear systems. This paper proposes a novel chaotification method for fractional order nonlinear systems based on the negative damping instability mechanism and fractional calculus technique. We then apply it to chaotify the fractional order Lorenz system with order lying in (1,2), which is stable originally with specific parameters. Moreover, we introduce three critical effective orders to distinguish different four dynamics: singleton sets attractor, self-excited attractor, coexisting attractors, and blow up behavior. Many simulations are carried out to illustrate the effectiveness of the results.