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In this paper, a new strategy is developed for controlling chaos and hyperchaos in a nonlinear system via switching modulation of systems parameters. The control method is illustrated by examples of the third-order chaotic Chua's circuit and a sixth-order coupled hyperchaotic Chua's circuit. Numerical simulations show that this method is very effective.

In this paper, we numerically investigate the chaotic behaviors of the fractional-order Chua's circuit with a piecewise-linear nonlinearity. We find that chaos exists in the fractional-order Chua's circuit with order less than 3. The lowest order we find to have chaos is 2.7 in the homogeneous fractional-order Chua's circuit and 2.8 in the unhomogeneous fractional-order Chua's circuit. Our results are validated by the existence of a positive Lyapunov exponent. A chaos synchronization method is also presented for synchronizing the homogeneous fractional-order chaotic Chua's systems. The approach, based on stability theory of fractional-order linear systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

A new method for generating the multi-scroll chaotic attractors is introduced. It is demonstrated that the multi-scroll chaotic attractors can be generated using the saw-tooth function series and different number of scrolls can be designed easily by modifying the natural number n of the saw-tooth function. Various scroll attractors are illustrated not only by computer simulation, but also by the realization of an electronic circuit experiment on EWB.

In this paper, an experimental study of practical realization to transmit private binary signals using chaos is presented. In particular, we use a Generalized Hamiltonian forms approach to synchronize two unidirectionally coupled Chua's circuits with the receiver being given by an observer. Experimental results are in close accordance with the numerical simulations.

In this paper, we continue our study of rank one chaos in switch-controlled circuits. Periodically controlled switches are added to Chua's original piecewise linear circuit to generate rank one attractors in the vicinity of an asymptotically stable periodic solution that is relatively large in size. Our previous investigations relied heavily on the smooth nonlinearity of the unforced systems, and were, by large, restricted to a small neighborhood of supercritical Hopf bifurcations. Whereas the system studied in this paper is much more feasible for physical implementation, and thus the corresponding rank one chaos is much easier to detect in practice. The findings of our purely numerical experiments are further supported by the PSPICE simulations.

This paper explores the use of notch filters for the purpose of damping out chaotic oscillations. The design of the filter and the way it is interfaced to the system are investigated from a signal-processing point of view. A Chua's circuit, that has typical applications in synchronization and secure communications, is used to exemplify the suggested methodology where both theoretical and experimental results are provided. The power spectrum of the original system is analyzed to selectively damp-out portions of the power spectrum, thus truncating period-doubling, the original cause of chaos. Both single and double notch filters are explored to examine their effect on the performance of the modified system. Steady state analysis as well as issues regarding practical implementation are addressed and advantages and limitations of the proposed method are highlighted.

The famous chaotic circuit known as Chua's oscillator, despite the robustness of the chaotic behavior to parametric mismatches, requires the construction of noncommercial valued inductor. A low cost inductorless version of Chua's oscillator is presented. The chaotic behavior of the circuit is verified by PSpice simulation and also by experimental study on a circuit breadboard. The results lead to excellent agreement with each other and with the results of previous investigators. Experimental results on the possibility of controlling chaos in the modified Chua's oscillator by the inherent feedback mechanism are also reported.

This paper introduces chaotic reference model-based dynamical state feedback chaotification method which can be applied to any input-state linearizable (nonlinear) system including linear controllable ones as special cases. In the developed method, any chaotic system of arbitrary dimension can be used as the reference model with no need to transform it into a special form, so providing the advantage of exploiting the vast amount of information on chaotic systems and their implementations available in the literature. To demonstrate the potential effective applications of the method, a permanent magnet dc motor is chaotified by the proposed dynamical state feedback as matching the closed loop dynamics to the well-known Chua's chaotic circuit. Then, an impeller mounted on the chaotified dc motor is used for mixing a corn syrup added acid–base mixture. It is observed in a nonintrusive way that mixing actuated by the chaotified dc motor is more efficient than constant and also periodical motor speed cases for the consideration of neutralization time and power consumption together.

This paper presents the design of novel autonomous and non-autonomous inductorless chaotic circuit using lambda diode. The autonomous chaotic circuit is implemented using Chua’s circuit, where the piece-wise linear element of Chua’s circuit called Chua’s diode is replaced by lambda diode. The lambda diode used as a nonlinear resistor in Chua’s circuit comprises of BJT, FET and resistors. The non-autonomous chaotic circuit is studied by replacing the piece-wise linear element of Murali–Lakshmana–Chua (MLC) circuit by lambda diode. The reason for employing lambda diode is that it has a wide range of negative resistance characteristics, which enable the circuit to operate at higher frequency ranges. The resulting chaotic oscillator can easily be made to operate at both low and high frequencies. The chaotic behavior of the circuit is established through Multisim simulations in the time and frequency domains. Both theoretical analysis and electronic circuit experiments are presented. The circuit’s chaotic characteristics are further confirmed by means of Poincare plot and the Bifurcation diagram. The observed route to chaos is period-adding.

A low voltage low power fully integrated chaos generator is presented in this paper. Comparing with the conventional off-the-shelf electronic components-based chaos generators, the designed circuit is fully integrated, and it achieves lower supply voltage, lower power dissipation and smaller chip area. The proposed fully integrated chaos generator is verified with GlobalFoundries 0.18$\mu$m CMOS 1P6M RF process using Cadence IC Design Tools. The simulation results demonstrate that the fully integrated chaos generator consumes only 17mW from $\pm$2.5V supply voltage. Moreover, the chip area of the chaos generator is only 1.755mm² including the testing pads, and it has a wide range of practical application prospects.

In this paper we present two different examples of electromechanical realization of Chua's circuit and one of Chua's unfolding circuit. In addition, a novel mechanism is proposed for realizing Chua's equations in a purely mechanical way using friction properties. All relevant equations are derived and the mechanical realizations of the proposed devices are discussed.

In this paper, a sliding mode controller is applied to control the cubic Chua's circuit system. The sliding surface of this paper used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specification and use less control energy by comparing with the result in the current existing literature. The results show that the proposed controller can steer Chua's circuit system to the desired state without the chattering phenomenon and abrupt state change.

In this Letter a feedback linearizing adaptive control system for the control of Chua's circuits is presented. It is assumed that all the parameters of the system are unknown. Using a backstepping design procedure, an adaptive control system is designed which accomplishes trajectory control of the chosen node voltage by an independent voltage source. Simulation results are presented which show precise trajectory tracking and regulation of the state vector to the desired terminal state.

In this paper, the stability of observer-based chaotic communications using Lur'e systems is presented. In this approach, the transmitter contains a chaotic oscillator with an input that is modulate by the information signal. The receiver is composed by a copy of the transmitter driven by a synchronization signal. Some effects of transmission noise on the demodulation procedure are discussed. Numerical simulations on Chua's circuit are provided to illustrate our findings.

An interdisciplinary analysis is presented in this paper on the relationship between the bifurcation behavior of chaotic systems, specifically Chua's circuit, and the quantized energy level of atoms. We show that it is possible to associate special capacitance values in Chua's circuits with the electronic energy levels E_n of atoms calculated from Bohr's Law. In particular, these particular capacitance values correspond to the bifurcation points α_n of Chua's circuits. We found a functional relation associating a specific Chua's circuit to the Hydrogen atom and obtained a map of "Atom" to " Chua's Circuit". This map can be extended to other elements in the Periodic Table, thereby demonstrating an almost universal relation between the two different physical systems. With this map we can calculate the energy levels of different atoms from bifurcation diagrams (or vice-versa) and express the analytical relations in terms of the two variables α_n and E_n.

In this paper, we demonstrate that some hyperchaotic circuits can be synchronized by using only one state variable. We applied three kinds of synchronization schemes, a continuous synchronization, an impulsive synchronization, and a selective synchronization to these hyperchaotic circuits. Their performance is examined from the viewpoint of synchronization stability and convergence time.

We propose a simple continuous-time system for chaos generation based on a third-order abstract canonical mathematical model. Nonlinearity in this model is introduced by a bipolar switching constant, which reflects the behavior of a digital inverter. A simple area efficient implementation of the system in a 1.2 μ CMOS process is presented. Experimental results from a tested chip are shown.

This letter shows an experimental suppression of spatial instability in one-way open coupled Chua's circuits. A continuous-time version of the decentralized delayed feedback method is used for a suppression scheme. Furthermore, we confirm that the control method also succeeds in suppressing chaotic behavior in the coupled circuits.

This paper presents a new approach to the design of a composite sliding mode control for a class of chaotic systems with uncertainties. A significant feature of this control scheme is the incorporation of a new complementary sliding variable to the conventional sliding variable in order that a high-performance controller can be obtained. It has been shown that the guaranteed steady-state error bounds are reduced by half, as compared with the conventional sliding control. Moreover, the dynamic responses during the reaching phase are also significantly improved. We used a controlled uncertain Lorenz system and a controlled uncertain Chua's circuit as illustrative examples to demonstrate the effectiveness of the design.

Several realizations of Chua's circuit have been proposed in the literature. The methodologies used in these realizations can be divided into two basic categories. In the first approach, a variety of circuit topologies have been considered for realizing the nonlinear resistor, N_R in Chua's circuit. The main idea in the second approach related to the implementation of the circuit is an inductorless realization of Chua's circuit. For this purpose, several circuit topologies serving as a synthetic inductor, i.e. inductance simulator, are used instead of the inductor element in Chua's circuit. In this study, after comparing the circuit topologies proposed for Chua's diode and the inductor element in the circuit, we will present six alternative hybrid realizations of Chua's circuit combining circuit topologies proposed for the nonlinear resistor and the inductor element in the literature. The PSpice simulation experiments confirm that the six alternative hybrid realizations of the circuit exhibit the original chaotic behavior of Chua's circuit.