Free control of a chaotic signal means that its various aspects such as amplitude, frequency and offset can be freely controlled, which is of great value for the application of chaotic circuits. However, such a chaotic circuit typically contains many quadratic terms requiring multiplier-oriented operations, which posts a great challenge to the design of chaotic oscillators. In this brief, a chaotic oscillator with easy free control containing five quadratic terms was designed and implemented. By making full use of the current output characteristic of multiplier AD633 and op-amp AD844, a compact chaotic circuit with three multipliers and only one op-amp was constructed. Experimental result shows its flexibility for free control.
In the chaotic Lorenz system, Chen system and R\"ossler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any preassigned number of equilibria. First, a chaotic system with no equilibrium is presented and discussed. Then, a methodology is presented by adding symmetry to a new chaotic system with only one stable equilibrium, to show that chaotic systems with any preassigned number of equilibria can be generated. By adjusting the only parameter in these systems, one can further control the stability of their equilibria. This result reveals an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of a chaotic system.
By constructing a suitable Lyapunov function, we show that for the system parameters in some specified regions, the solutions of the Chen system are globally bounded.
In this paper, we present a ‘smart’ neural control scheme for uncertain non‐linear systems using the localized radical basis function (RBF) networks. This scheme is designed such that the current control action can utilize the knowledge that the NN learned from the past control process. Compared with most existing adaptive neural controllers, which are in general very‐high‐order dynamic controllers due to the simultaneous adaptation of a large number of neural weights, the smart RBF neural controller is a static and low‐order one, and thus is more computationally feasible in practical design and implementation. To improve the generalization ability of the RBF networks, which plays an important role in the smart neural control scheme, chaotic reference signals are employed in the training phase of the scheme, where the complex chaotic signals offer richer information for NN learning due to the ergodicity of chaos. The proposed neural control scheme can act ‘smartly’ in the operational phase after the RBF networks have been well‐trained in the training phase, in a way similar to the process that humans accomplish some complicated control tasks easily after the ‘neuro‐controllers’ in their brains have been well‐trained previously. The smart neural control scheme also provides a strong motivation for the current research on chaos generation. Simulation studies are included to demonstrate the effectiveness of the new control scheme. Copyright © 2003 John Wiley & Sons, Ltd.
No abstract is provided for this article.
There exist some fundamental and yet challenging problems in pinning control of complex networks: (1) What types of pinning schemes may be chosen for a given complex network to realize synchronization? (2) What kinds of controllers may be designed to ensure the network synchronization? (3) How large should the coupling strength be used in a given complex network to achieve synchronization? This paper addresses these technique questions. Surprisingly, it is found that a network under a typical framework can realize synchronization subject to any linear feedback pinning scheme by using adaptive tuning of the coupling strength. In addition, it is found that the nodes with low degrees should be pinned first when the coupling strength is small, which is contrary to the common view that the most-highly-connected nodes should be pinned first. Furthermore, it is interesting to find that the derived pinning condition with controllers given in a high-dimensional setting can be reduced to a low-dimensional condition without the pinning controllers involved. Finally, simulation examples of scale-free networks are given to verify the theoretical results.
The power of unofficial groups sometimes is stronger than official groups in the organization. The key persons in the network of organization also can help manage effectively. This research used social network analysis to investigate the effect between Facebook and LINE. We also used three indicators of degree centralities to infer the power on different social network. The results revealed the members have official position are not necessary in the center of the social network. The influence of message delivery is stronger from unofficial groups. The findings also showed key persons from unofficial groups may help companies efficiently manage firms.
We study synchronization and desynchronization of a complex network of chaotic dynamical systems, in both continuous-time and discrete-time cases. With proved synchronization conditions, we illustrate network synchronization and desynchronization processes by a prototype composing of Henon maps in a scale-free network. We show that synchronization and desynchronization of such a complex dynamical network can be determined by the network topology and the maximum Lyapunov exponent of the individual chaotic nodes.
This paper outlines a fuzzy formulation and its solutions for a path-planning problem. In this fuzzy approach, a workspace can be either a finite or infinite collection of discrete points with each representing a fuzzy set. The path-planning problem is formulated as a fuzzy optimization problem where the cost to be minimize representing the length of the path connecting two fuzzy sets representing the source and destination. There are two approaches to treating obstacles: formulating the fuzzy membership function of the fuzzy sets representing the area occupied by obstacles into the constraints, and formulating the fuzzy cost function with stiff penalty in using these fuzzy sets representing the area occupied by obstacles. Solutions are derived and numerical simulations are presented to verify the theoretical results.
This paper demonstrates that complex dynamical behaviors such as limit cycles and chaotic invariant sets can exist in some simple autonomous hybrid planar systems governed by simple transition laws.