Chaos Control Of Low-dimensional Systems In A Timely Manner - Pattern Of The Empty System Dynamics,

The paper investigates the characteristic of frequency in nonlinear autonomous chaotic systems, controlling chaos via the viable time-delayed feedback control (DFC) method, improving the efficiency of DFC method through linear invertible transform, noose target and target waves and spatial disorder under different conditions in the two coupled lattices.The characteristic of frequency in some low-dimensional systems and second-order continuous delayed chaotic systems (i.e. infinite-dimensional chaotic systems, formulated and chosen by computing the maximum Lyapunov exponent) have been studied numerically. We find the relations between the parameters and systemic periods and the connection among different systemic periods. In addition, the practical methods of the theory of Hopf bifurcation are applied to analyze some essential systemic parameters, such as the critical point at which the periodical solution appear, the approximation of the foundational period, the stability and direction of Hopf bifurcation.We analytically determine some general conditions of time-delayed feedback control of three-dimensional autonomous chaotic systems. With this method, a criterion for the stability of periodic solution under control and for the direction of Hopf bifurcation is derived theoretically studied. Applying the method to control some three-dimensional autonomous chaotic systems, the feasibility of the analytic results is confirmed.A scheme, which can be used to effectively improve the quality of time-delayed feedback control of chaos, is proposed based on linear invertible transform. Through transforming parts of the system state variables in the corresponding sub-space, we can successfully control chaos with single time-delayed feedback signal instead of multi-signals in the originate system before the transformation. Therefore, the conditions that ensure the system would be stabilized can be found theoretically. A novel noose target method, being both simple and convenient, is advanced. The method can be used to target chaos in discrete and continuous systems. Therefore, it is able to lead the chaotic orbit to the neighborhood of the target or hit the target directly in very short time.Two systems of two coupled lattices are formed in an oscillatory media composing of chaotic Chen and Lorenz system respectively. We find target waves in the coupled lattices and different types of transitions to spatial disorder under different conditions via numerical analysis. The analytic and numeric methods are integrated closely in this paper. The results above are significant in the effective controlling chaos and the further research of the pattern dynamics in the reaction-diffusion systems.