By combining the technique of observer design in nonlinear control systems theory and the technique of phase space reconstruction in nonlinear dynamical systems theory, we show that synchronization of smooth (hyper)chaotic systems can be attained with any scalar transmitted signal. The proposed method has been illustrated via two examples.

Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions are in the power-law form. In this paper, we investigate the synchronization phenomenon in scale-free dynamical networks.We show that if the coupling strength of a scale-free dynamical network is greater than a positive threshold, then the network will synchronize no matter how large it is. We show that the synchronizability of a scale-free dynamical network is robust against random removal of nodes, but is fragile to specific removal of the most highly connected nodes.

It is now known that the complexity of network topology has a great impact on the stabilization of complex dynamical networks. In this work, we study the control of random networks and scale-free networks. Conditions are investigated for globally or locally stabilizing such networks. Our strategy is to apply local feedback control to a small fraction of network nodes. We propose the concept of virtual control for microscopic dynamics throughout the process with different pinning schemes for both random networks and scale-free networks.We explain the main reason why significantly less local controllers are required by specifically pinning the most highly connected nodes in a scale-free network than those required by the randomly pinning scheme, and why there is no significant difference between specifically and randomly pinning schemes for controlling random dynamical networks. We also study the synchronization phenomenon of controlled dynamical networks in the stabilization process, both analytically and numerically.

A time-delay feedback control approach is developed for making a continuous-time minimum-phase system chaotic. The approach is based on the geometric control theory and a suitable approximate relationship between a time-delay differential equation and a discrete map. If the original system has an exponentially stable equilibrium point, then a simple time-delay output-feedback controller with arbitrarily small amplitude can drive the system chaotic. Two different types of simulation examples are included for demonstration.

This brief proposes a unified approach for generating chaos in -dimensional continuous-time affine systems, with 3, based on the normal form of chaotic systems and nonlinear control theory. A feedback-control law is designed to make a feedback linearizable system topologically conjugate to a reference chaotic system, thereby forcing the given system to become chaotic. Furthermore, if the relative degree of a given feedback unlinearizable system is not less than three and the corresponding internal dynamics of the system is input-to-state stable, then a feedback-control law can still be designed to drive a subsystem of such a controlled system topologically conjugate to a reference chaotic system, thereby generating chaos from that subsystem.