Narrow Results

This paper proposes a linear adaptive state feedback controller which achieves asymptotic tracking of the controlled cubic Chua's system. The gain vector is tuned using an adaptation law derived using the Lyapunov stability theory. The aim is to design an adaptive controller that mimics a predetermined input–output linearizing controller known for its effective performance in output tracking. We show that the system model is not necessary to construct the controller. We also show that synchronization of two cubic Chua's systems can be achieved. Numerical simulations are presented to illustrate the efficiency of the proposed scheme.

A new circuit configuration, linearly conjugate to the standard Chua's circuit, is presented. Its distinctive feature is that the equations now admit an additional parameter, which controls the dissipation in the network connected to the Chua diode. In the limiting case we obtain the simplest chaotic circuit, consisting of a piecewise-linear resistor and three lossless elements.

We use the Poincaré compactification for a polynomial vector field in ℝ³ to study the dynamics near and at infinity of the classical Chua's system with a cubic nonlinearity. We give a complete description of the phase portrait of this system at infinity, which is identified with the sphere 𝕊² in ℝ³ after compactification, and perform a numerical study on how the solutions reach infinity, depending on the parameter values. With this global study we intend to give a contribution in the understanding of this well known and extensively studied complex three-dimensional dynamical system.

The problem of global synchronization control for a class of new Chua's system is studied in this paper. Several linear controllers are proposed to realize the global exponential synchronization of two Chua's systems. Decoupling feedback control method is used to make Chua's system global exponential synchronized. Global exponential synchronization with respect to (w.r.t) partial state variables is studied when one of the error variables is zero. Finally, an adaptive synchronization controller is designed to make the response and the driven systems synchronized. Moreover, the estimate errors of the uncertain parameters converge to zero since the persistent excitation condition holds. Additionally, numerical simulations show the effectiveness of the proposed controllers.

In this paper, chaos in complex-order Chua’s system and its chaotic synchronization for secure communication are studied based on the fractional derivative investigated. Chaos in complex-order Chua’s system is illustrated by presenting its waveform graphs, states diagrams and bifurcation graphs. The dynamic behaviors in the complex-order Chua’s system and time-delayed Chua’s system are compared. In addition, the largest Lyapunov exponents of normal and time-delayed Chua’s systems are calculated and verified by numerical simulations. The experiment indicates that the chaos in such Chua’s system can achieve two channel communications.