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.

A time-delay chaotification approach can be applied to the Chua's circuit by adding a small-amplitude time-delay feedback voltage to the circuit. The chaotic dynamics of this newly derived time-delay Chua's circuit is studied by theoretical analysis, verified by computer simulations as well as by circuit experiments.

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.

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.

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure.