A New Chaotic oscillator generated from the Duffing Analysis and chaos control

In this paper a chaotic system with nine terms and three quadratic non linearities is proposed. The new
$3-D$
chaotic oscillator generated from the
$2-D$
Duffing one, obtained by adding a nonlinear state feed- back to the first equation and a cross-product term to the second one, with two new optimized additive control parameters. Basic dynamical properties of the proposed system are analyzed by means of phase portraits, stability of equilibrium, Lyapunov exponent and bifurcation. The new system has four lymit cycles, the unforced model has four equilibirium points, three Lyapunov exponents
$L_{1}=1.670798;L_{2}=-1$
: 421639;
$L_{3}=-9$
: 999158, which show a chaotic behavior. The bifurcation plots for all system's parameters show denser points confirming the existence of the parameter dependence of system. Also, the proposed system is controlled using a genetically optimized control bazed on Lyapunov function(CLF).