Mohammed-Salah Abdelouahab

Abstract: Abstract In this work, a new three-dimensional autonomous chaotic system has been introduced by modifying a hybrid optical system. The single quadratic nonlinearity is replaced by a single cubic nonlinearity; the new system can display two 1-scroll chaotic attractors simultaneously or one 2-scroll chaotic attractor.ThebifurcationdiagramisobtainedandLyapunov spectrum is calculated for the proposed system. The results show that the new system exhibits rich complexity features such as stable, periodic, and chaotic dynamics.

Abstract: Fractional-order �nancial system introduced by W.-C. Chen 2008 displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreover numerical simulations are shown to verify the e�ectiveness of the proposed control scheme.