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The synchronization control of Lu chaotic systems is focused on this paper, by using the controller designed by Zhang dynamics (ZD) method, with only one input. The ZD method is a handy and simple method for designing control input. The controller, designed by ZD method, is able to synchronize Lu chaotic systems. Engineering-type steady-state analysis is given to confirm the efficacy of the controller...
This paper aims at achieving the stabilization control of hyper-chaotic Lu system with only one control input. By employing Zhang dynamics (ZD) method, which is a simple and effective method for designing control input, the expression of the desired controller is thus obtained. This easy-to-design controller, synthesized by following specific steps of ZD design method, is able to stabilize the 4th-order...
The tracking-control problem of a special nonlinear system (i.e., the extension of a modified Lorenz chaotic system) with additive input or the mixture of additive and multiplicative inputs is considered in this paper. It is worth pointing out that, with the parameters fixed at some particular values, the modified Lorenz nonlinear system degrades to the modified Lorenz chaotic system. Note that, due...
Solving nonlinear equations has become increasingly significant and indispensable in many disciplines. In the recent decade, two powerful methods, the Zhang dynamics (ZD) method and the gradient dynamics (GD) method have been extensively investigated and implemented in solving nonlinear equations. In addition, some conventional methods, such as the dynamic relaxation method (DRM), redundant manipulators...
In this paper, a discrete-time Zhang neural network (DTZNN) model, discretized from continuous-time Zhang neural network, is proposed and investigated for performing the online future minimization (OFM). In order to approximate more accurately the 1st-order derivative in computation and discretize more effectively the continuous-time Zhang neural network, a new Taylor-type numerical differentiation...
Russia population problem attracts great concerns to the future trend of population and the development of the nation. Conventional researches on Russia population prediction are usually based on the standard cohort-component method. Such a method only allows for several factors (fertility, mortality and migration rates), and then leads to the lack of all-sidedness in the prediction results. With...
As one of the most important factors influencing the development potential of the country, China's population attracts considerable attention. Some official organizations regularly publish the predictions of China's population every calendar year. However, most of the predictions use the standard cohort-component method, which does not allow for all relevant impact factors and may lose sight of some...
This paper considers solving the tracking and stabilizing control problems of the Chen chaotic system with multiplicative inputs. By using the Zhang-gradient (ZG) method, which combines Zhang dynamics (ZD) and gradient dynamic (GD), a ZG controller is obtained for solving the problems above. Moreover, another new ZG controller is designed by using the ZG method again. Simulation results further show...
The paper employs gradient dynamics (GD), in addition to Zhang dynamics (ZD), to generate new fractals which are quite different from the conventional Newton fractals (NF). The proposed gradient fractals (GF) have three types. Specifically, via appropriate iterative formulas derived in complex domain, the first-type and second-type fractals are generated, i.e., 1GF and 2GF. By expanding the conventional...
The Runge phenomenon illustrates that equidistant polynomial interpolation of the Runge function will cause wild oscillation near the endpoints of the interpolation interval as the order of the interpolation polynomial increases. In this paper, the pseudo inverse cubic spline (PCS) is presented to accurately approximate the Runge function at equidistant interpolation nodes and solve the problem of...
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