Fractional-order financial 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 effectiveness of the proposed control scheme.
Contrary to integer order derivative, the fractional-order derivative of a nonconstant periodic function is not a periodic function with the same period, as a consequence of this property the time-invariant fractional order system does not have any non-constant periodic solution unless the lower terminal of the derivative is ±∞, which is not practical. This property limits the applicability areas of fractional derivatives and makes it unfavorable, for a * corresponding author Email addresses: medsala3@yahoo.fr (Mohammed-Salah Abdelouahab), n.hamri@centre-univ-mila.dz (Nasr-Eddine Hamri)
Recently, chaos theory has been used in the development of novel techniques for global optimization , and particularly, in the specification of chaos optimization algorithms (COA) based on the use of numerical sequences generated by means of chaotic map.In this paper, we present an improved chaotic optimization algorithm using a new two-dimensional discrete multifold mapping for optimizing nonlinear functions(ICOMM). The proposed method is a powerful optimization technique, which is demonstrated when three nonlinear functions of reference are minimized using the proposed technique.
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. The bifurcation diagram is obtained and Lyapunov 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.
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