In this paper, we propose a robust state estimation method using a particle filter (PF) for a class of nonlinear systems which have stochastic parameter uncertainties. A robust PF was designed using prediction and correction structure. The proposed PF draws particles from a simple proposal density function and corrects the particles with particle-wise correction gains. We present a method to obtain an error variance of each particle and its upper bound, which is minimized to determine the correction gain. The proposed method is less restrictive on system nonlinearities and noise statistics; moreover, it can be applied regardless of system stability. The effectiveness of the proposed robust PF is illustrated via an example based on Chua's circuit.

Memristor is drawing more and more attraction nowadays after HP Laboratory announced its invention. Since then many researchers are taking efforts to find its applications in various areas of the information technology. Among the important applications, one of the interesting issues is the research on memristor circuits. To put forward such research, there is an urgent demand to establish a memristor SPICE model, such that people could conduct SPICE simulation to obtain the performance of the memristor circuits under their investigation. This paper reports our efforts to meet the urgent demand. Based on the memristor device fabrication technology parameters, as well as the theoretical description on memristor, we first propose memristor SPICE models, then verify the effectiveness of the proposed models by applying it to some memristor circuits. Simulation results are satisfactory.

The problem of designing a robust adaptive control for nonlinear systems with uncertain time-varying parameters is addressed. The upper bound of uncertain parameters, considered even in control coefficients, are not required to be known. An adaptive tracking controller is presented and, using the Lyapunov theory, the closed-loop stability and tracking error convergence is shown. In order to improve the performance of the method, a robust mechanism is incorporated into the adaptive controller yielding a robust adaptive algorithm. The proposed controller guarantees the boundedness of all closed-loop signals and robust convergence of tracking error in spite of time-varying parameter uncertainties with unknown bounds. The parametric uncertain systems under consideration describes a wide class of nonlinear circuits and systems. As an application, a novel parametric model is derived for nonlinear Chua's circuit and then, the proposed method is used for its control. The effectiveness of the method is demonstrated by some simulation results.

In this paper the attention is focused on the numerical study of hyperchaotic 2D-scroll attractors via the Adomian decomposition method. The approach, which provides series solutions of the system equations, is first applied to weakly-coupled Chua's circuits with Hermite interpolating polynomials. Then the method is successfully utilized for achieving hyperchaos synchronization of two coupled Chua's circuits. The reported examples show that the approach presents two main features, i.e., the system nonlinearity is preserved and the chaotic solution is provided in a closed form.

The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the origin in the Chua's equation with a cubic nonlinearity is carried out. The local analysis provides, in first approximation, different bifurcation sets, where the presence of several dynamical behaviours (including periodic, homoclinic and heteroclinic orbits) is predicted. The local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of the normal form of the Takens-Bogdanov bifurcation shows the presence of a degenerate (codimension-three) situation, which is analyzed in both homoclinic and heteroclinic cases.

In this paper, a new digital chaos circuit which can generate multiple-scroll strange attractors is proposed. Being based on the piecewise-linear function which is determined by on-chip supervised learning, the proposed digital chaos circuit can generate multiple-scroll strange attractors. Hence, the proposed circuit can exhibit various bifurcation phenomena. By numerical simulations, the learning dynamics and the quasi-chaos generation of the proposed digital chaos circuit are analyzed in detail. Furthermore, as a design example of the integrated digital chaos circuit, the proposed circuit realizing the nonlinear function with five breakpoints is implemented onto the FPGA (Field Programmable Gate Array). The synthesized FPGA circuit which can generate n-scroll strange attractors (n=1, 2, 4) showed that the proposed circuit is implementable onto a single FPGA except for the SRAM.

In this paper, we demonstrate how Yamakawa's chaotic chips and Chua's circuits can be used to implement a secure communication system. Furthermore, their performance for the secure communication is discussed.

In this letter a new method for controlling chaos is proposed. Although different several methods based on the OGY- and the OPF-method perturb a value of an accessible system parameter, the proposed method perturbs the only timing of switching three values of a parameter. We apply the proposed method to the well-known Chua's circuit on computer simulations. The chaotic orbits in the Rössler type- and the double scroll type-attractor can be stabilized on several unstable periodic orbits embedded within these attractors.

More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol.40, no.10, October 1993), an International workshop on "Chua's Circuit: chaotic phenomena and applications" at NOLTA'93, and a book (Edited by R. N. Madan, World Scientific, 1993) on Chua's circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last 6 months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua's circuit. The robustness of this IC chip demonstrates that an array of Chua's circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua's circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua's circuit--now generally referred to as Chua's oscillator. This circuit is most significant because it is structurally the simplest (it contain only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21–parameter family of continuous odd–symmetric piecewise–linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua's Circuits, e.g., stochastic resonance, chaos–chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua's circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua's circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g., secure communication.

New communication systems via chaotic modulations are experimentally, demonstrated. They contain the wellknown chaotic circuits as its basic elements--Chua's circuits and canonial Chua's circuits. The following advantage is found in our laboratory experiments: (a) Transmitted signals have broad spectra. (b) Secure communications are possible in the sense that the better parameter matching is required in order to recover the signal. (c) The circuit structure of our communication system is most simple at this stage. (d) The communication systems are easily built at a small outlay.

By adding a linear resistor in series with the inductor in Chua's circuit, we obtain a circuit whose state equation is topologically conjugate (i.e., equivalent) to a 21-parameter family C of continuous odd-symmetric piecewise-linear equations in R3. In particular, except for a subset of measure zero, every system or vector field belonging to the family C, can be mapped via an explicit non-singular linear transformation into this circuit, which is uniquely determined by 7 parameters. Since no circuit with less than 7 parameters has this property, this augmented circuit is called an unfolding of Chua's circuit--it is analogous to that of "unfolding a vector field" in a small neighborhood of a singular point. Our unfolding, however, is global since it applies to the entire state space R3. The significance of the unfolded Chua's Circuit is that the qualitative dynamics of every autonomous 3rd-order chaotic circuit, system, and differential equation, containing one odd-symmetric 3-segment piecewise-linear function can be mapped into this circuit, thereby making their separate analysis unnecessary. This immense power of unification reduces the investigation of the many heretofore unrelated publications on chaotic circuits and systems to the analysis of only one canonical circuit. This unified approach is illustrated by many examples selected from a zoo of more than 30 strange attractors extracted from the literature. In addition, a gallery of 18 strange attractors in full color is included to demonstrate the immensely rich and complex dynamics of this simplest among all chaotic circuits.