Dynamical Analysis And Chaos Control Of A New System Based On Unified Lorenz-type System

This paper produce a CC-ML system, which is based upon unified Lorenztype system. The system contains as special cases the conjugate Chen system andmodified Lorenz system. In this paper, complicated dynamical behaviors of thesystem is investigated comprehensively by rigorous mathematical analysis and symbolic computation. Firstly, its stability properties of equilibrium are investigatedby the center manifold theory. Then the conditions of Hopf bifurcation is obtained.Secondly, the stability of periodic solutions and direction of Hopf bifurcation areanalyzed by means of the Hopf bifurcation theorem. Thirdly, based on Matlabsoftware, some complicated dynamical behaviors of CC-ML system in the parametric space is numerically displayed by phase portrait, Poincarémappings and powerspectrum and so on. At the same time, some properties of chaotic attractor aredemonstrated by Lyapunov esponents and fractional dimensions. Further, we add aconstant controller to the second equation in the CC-ML system. Compound structures of CC-ML chaotic attractor are displayed by some phase portraits. Which areboth obtained by merging together two simple attractors-the left and right attractorsafter performing a mirror operation. Finally, chaos control is investigated in the final chapter. Linear feedback control is used to suppress chaotic behavior of CC-MLsystem to unstable equilibrium points and arbitrary periodic orbit, and numericalsimulations are carried out to investegate the controlled system. Furthermore, viathe nonsingular transformation, it is shown that the Dufffing oscillator with a statefedback control is diffeomorphic to the special cases of CC-ML system- -conjugateChen system and modified Lorenz system.