This paper studies the problem of controlling chaos in Lorenz system. By dividing Lorenz system into two subsystems, the small gain theorem is used to design linear feedback controllers to make the equilibrium points of the controlled system globally asymptotically stable. Thus chaos in Lorenz system disappears under the controller.

1 Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons 1], lasers 2], chemical reactions 3], arrhythmic cardiac tissue 4], and spontaneously bursting neuronal networks 5]. An underlying assumption in all of these studies is that the system being controlled is chaotic. However, the identiication of chaos in experimental systems, ...

Abstract – A chaos control method suggested by Erjaee has been reviewed. It has been shown that this technique can be applied in various evolutionary systems of 2-dimensional types. The method has been applied for cases of the Henon map, as well as Burger’s map. The limitations of the control technique have also been discussed by considering the Standard Map and the Gumowski-Mira map. The resul...

By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the behavior and performance of the stabilized algorithm. Typeset using REVTEX

The problem of ordering chaos by second-order sliding-mode control is addressed. The proposed approach offers an effective, yet simple, solution tackling both the uncertainties affecting the chaotic dynamics and the measurement noise corrupting the feedback signals. The procedure is illustrated making reference to Chua's circuit and the “suboptimal” second-order sliding-mode control algorithm. ...

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term cr...

We present a method allowing one to partly stabilize some chaotic Hamiltonians which have two degrees of freedom. The purpose of the method is to avoid the regions of V(q(1),q(2)) where its Gaussian curvature becomes negative. We show the stabilization of the Hénon-Heiles system, over a wide area, for the critical energy E=1/6. Total energy of the system varies only by a few percent.

We find a dynamic effect in the non-equilibrium dynamics of spin glass that closely parallels equilibrium temperature chaos. This effect, we name chaos, is spatially heterogeneous to large degree. The key controlling quantity time-growing spin-glass coherence length. Our detailed characterization chaos paves way for analysis recent and forthcoming experiments. work has been made possible thanks...