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The impulsive synchronization of two chaotic Chen–Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen–Lee systems was also implemented using an electronic circuit.

In this paper, we extend the topological formulae of Maxwell and Kirchhoff, characterizing the non-singularity of node-admittance and loop-impedance matrices, to mixed problems, that is, to circuits combining admittance and impedance descriptions or, in nonlinear cases, involving both voltage- and current-controlled resistors. By means of this mixed formula we analyze the index of differential-algebraic models of nonlinear uncoupled circuits in a very broad setting, namely, without assumptions on their topology, their passivity or the controlling variables for nonlinear resistors. In particular, our approach allows for a characterization of index two circuits in topologically degenerate settings, which had been so far elusive in the non-passive context. As a byproduct we address the unique solvability of mixed resistive circuits, a problem which also arises in connection to the so-called DC-solvability condition of dynamic circuits. For the sake of brevity, we discuss in less detail how to extend the analysis to problems with mixed descriptions in reactive devices.

A novel method of nodal impedance calculation is presented in this paper. This method is capable of time-efficient calculation of arbitrary two-point complex impedance in an analog and mixed-signal circuit and could improve the development time of impedance-based tests both in DC and AC domain. A fault simulation methodology based on the proposed method is described in detail. Several experiments are provided that prove the time efficiency of the method. Experimental application showing the benefits of the method on a real circuit is provided as well.

In this paper, a flux-controlled memristor with linear memductance is proposed. Compared with the memristor with piecewise linear memductance and the memristor with smooth continuous nonlinearity memductance which are widely used in the study of memristive chaotic system, the proposed memristor has simple mathematical model and is easy to implement. Multisim circuit simulation and breadboard experiment are realized, and the memristor can exhibit a pinched hysteresis loop in the voltage–current plane when driven by a periodic voltage. In addition, a new hyper-chaotic system is presented in this paper by adding the proposed memristor into the Lorenz system. The transient chaos and multiple attractors are observed in this memristive system. The dynamical behaviors of the proposed system are analyzed by equilibria, Lyapunov exponents, bifurcation diagram and phase portrait. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system.

Chaotic systems with a curve of equilibria have attracted considerable interest in theoretical researches and engineering applications because they are categorized as systems with hidden attractors. In this paper, we introduce a new three-dimensional autonomous system with cubic equilibrium. Fundamental dynamical properties and complex dynamics of the system have been investigated. Of particular interest is the coexistence of chaotic attractors in the proposed system. Furthermore, we have designed and implemented an electronic circuit to verify the feasibility of such a system with cubic equilibrium.

Following the experimental realization of memristors, researchers have focused on memristor-based circuits. Chaotic circuits can be implemented easily using a memristor due to its nonvolatile and nonlinear behavior. This study presents a memristor-based four-dimensional (4D) chaotic oscillator with a line equilibria. A memristor having quadratic memductance was utilized to implement the proposed chaotic oscillator. The 4D chaotic oscillator with quartic nonlinearity was designed as a result of the quadratic memductance. In terms of communication security, random number generation and image and audio encryption, systems with quartic nonlinearity or that are higher-dimensional are better than systems that are lower-dimensional or possess quadratic/cubic nonlinearity. The performance of the proposed chaotic circuit was investigated according to properties such as phase portraits, Jacobian matrices, equilibrium points, Lyapunov exponents and bifurcation analyses. Furthermore, the proposed system is multistable and its solutions tend to appear as twin attractors when initial conditions approach their equilibria. The Lyapunov-based nonlinear controller was constructed for controlling the proposed system having a line equilibria. The effect of the initial conditions on the controlling indicators was also studied. In conclusion, by using discrete circuit elements, the proposed circuit was constructed, and its experimental results demonstrated a good agreement with the simulation results.

We have proposed a process of generating fractals not from the results of chaotic dynamics, but from the switching of ordinary differential equations. This paper experimentally and numerically analyzes the dynamics of an electronic circuit driven by stochastically switching inputs. The following two results are obtained. First, the dynamics is characterized by a set Γ(C) of trajectories in the cylindrical phase space, where C is a set of initial states on the Poincaré section. Γ(C) and C are attractive and unique invariant fractal sets that satisfy specific equations. The second result is that the correlation dimension of C is in inverse proportion to the interval of the switching inputs. These two findings move beyond the conventional theory based on contraction maps. It should be noted that the set C is constructed by noncontraction maps.

This Letter studies adaptive chaos synchronization between two coupled nonlinear electrical circuits using a linear state feedback. A simple and yet easily applicable algorithm is derived for adaptive chaos synchronization based on the Lyapunov stability theory. An adaptive linear state feedback is derived such that the coupled systems are globally synchronized. Numerical simulations show the effectiveness of the proposed synchronization scheme. A Pspice simulation of the adaptive synchronization process is performed to confirm the numerical results.

The simplest electronic circuit with a memristor was recently proposed. Chaotic attractors solution to this memristive circuit are topologically characterized and compared to Rössler-like attractors.

An electronic circuit device, inspired on the FitzHugh–Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of the electronics quantitatively reproduces the experimental observations on the circuit, including the Hopf bifurcation at the onset of tonic spiking. Moreover, we have implemented an analog noise generator as a source to study the variability of the spike trains. When the circuit is in the excitable regime, coherence resonance is observed. At sufficiently low noise intensity the spike trains have Poisson statistics, as in many biological neurons. The transfer function of the stochastic spike trains has a dynamic range of 6 dB, close to experimental values for real olfactory receptor neurons.

Using the damped harmonic oscillator equations as a mathematical template, several novel chaotic oscillators are developed with an emphasis on mathematical simplicity and ease of electronic circuit implementation. These chaotic systems offer an intuitive introduction to chaos theory, enabling comparison of mathematical and computational analyses with experimental results.

Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.

A restriction of the use of lead in electronics can be expected. Conductive adhesives are able to replace the lead containing solder. The alternative joining technology should not only replace lead, debonding of the connection must be possible for the purpose of repair and recycling, too. Possible methods for debonding are described as well as requirements of environmentally friendly adhesively bonded electronics.