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This paper deals with a new fractional calculus based method to stabilize fixed points of single-input 3D systems. In the proposed method, the control signal is determined by fractional order integration of a linear combination of the system linearized model states. The tuning rule for this method is based on the stability theorems in the incommensurate fractional order systems. The introduced technique can be used in suppression of chaotic oscillations. To evaluate the performance of the proposed technique in practical applications, it has been experimentally applied to control chaos in two chaotic circuits.

Smart nonlinear circuits can be tamed to reproduce the main dynamical properties in neural activities and thus neural circuits are built to estimate the occurrence of multiple modes in electric activities. In the presence of electromagnetic radiation, the cardiac tissue, brain and neural circuits are influenced because field energy is injected and captured when induction field and current are generated in the media and system. In this paper, an isolated Chua circuit is exposed to external electromagnetic field and energy capturing is estimated for nonlinear analysis from physical viewpoint. Furthermore, two Chua circuits without direct variable coupling are exposed to the same electromagnetic field for energy capturing. Periodical and noise-like radiations are imposed on the Chua circuits which can capture the magnetic field energy via the induction coil. It is found that the two Chua circuits (periodical or chaotic) can reach phase synchronization and phase lock in the presence of periodical radiation. On the other hand, noise-like radiation can realize complete synchronization between two chaotic Chua circuits while phase lock occurs between two Chua circuits in periodical oscillation. It gives some important clues to control the collective behaviors of neural activities under external field.

Nowadays, many simulations, implementations, synchronization and secure communication applications of chaotic circuits have been introduced in literature. However, electronics circuit design and implementation of nonlinear Sprott Case H chaotic system and its synchronization were not found in the literature. In this paper, numerical model, electronics circuit simulation and implementation electronics circuits of the Sprott Case H chaotic system and its synchronization by the method of Pecora and Carroll (P–C) complete replacement (CR) were performed. The simulation and implementation results showed that the Sprott Case H chaotic system can be synchronized and thus can be used for secure communication and encryption applications.

A new chaotic circuit is practically realized, for the first time, using a Lambert W-function. The circuit consists of three main parts. The first part employs a well-known Wilson current mirror, whereas the second part is a simple resistor at the two connected emitters of the current mirror. Both parts form a new circuit for a Lambert W-function by enabling a term of an emitter current to be simultaneously appeared on both sides of an exponential equation. Such a nonlinear equation is particularly well suited for realization of a Lambert W-function. The third part exploits a capacitor–inductor–capacitor (CLC) network and a resistor, which are connected to the nonlinear circuit of the Lambert W-function to allow for chaotic oscillations. The new circuit is capable of both a Lambert W-function and a current-tunable chaotic oscillator.

When signum operation is applied in chaotic systems to realize piecewise-linearity, the original nonlinearity turns to be a kind of Boolean calculation, and correspondingly the chaotic circuit can be implemented by an analog structure embedded with some logic-gate circuits. In this paper, as examples based on the diffusionless Lorenz system we proposed a couple of chaotic flows with signum piecewise-linearity, which experimentally resorts to digital gate circuits. The experimental chaotic circuit with logic elements was built, and the oscillation in the physical circuit agrees well with the numerical simulation.

Electrical circuits based on linear and nonlinear modelling principles have difficulties to meet demands caused by a large amount of data generated and processed. The aim is to examine the existing models from bigeometric calculus point of view to obtain accuracy on the results. This work is an application of bigeometric Runge–Kutta (BRK4) method aiming to solve differential equations with nonzero initial condition. This type of work arises from applications where the systems are defined by ordinary differential equations such as noise, filter, audio, chaotic circuits, etc. Solutions to these types of equations are not always easy. The improvement in this work is obtained by introducing bigeometric calculus in the process of seeking a solution to differential equations. Different classes of input signals are applied as input to the system and processed to determine the accuracy of the output. The applicability is tested against the classical method called Runge–Kutta (RK4). Simulation results confirm the application of BRK4 method in electrical circuit analysis. The new method also provides better results for all types of input signals, i.e., linear, nonlinear, constant or Gaussian.

An exhaustive analysis of a four-wing chaotic system is presented in this paper. It is proved that the evolution range of some variables can be modulated easily by one coefficient of a cross product term. An amplitude-adjustable chaotic circuit is designed, which shows a good agreement with the theoretical analysis. Also, in this paper a microcontroller-based random number generator (RNG) was designed with a nonlinear four-wing chaotic system. RNG studies of the current time have been usually carried out with complicated structures that are costly and difficult to use in real time implementations and that require so much energy consumption. On the other hand, in this paper, as opposed to the disadvantages mentioned here, a microcontroller-based RNG was designed with a four-wing chaotic system (also discussed in the paper) and this was introduced to literature. Microcontroller-based random numbers that passed randomness tests will be available for use in many fields in real life, particularly in encryption.

In this study, a chaotic circuit suitable for an integrated circuit is proposed. The circuit consists of two CMOS ring oscillators and a pair of diodes. By using a simplified model of the circuit, the mechanism of generating chaos is explained and the exact solutions are derived. The exact expressions of the Poincaré map and its Jacobian matrix make those possible to confirm the generation of chaos using the Lyapunov exponents and to investigate the related bifurcation phenomena.

In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.

In this paper, a novel approach of using genetic algorithm towards the realization of Chua's circuit is presented. The paper demonstrates the use of genetic algorithm to evolve Chua's circuit from a set of given passive and active components. More than a dozen of the evolved designs are demonstrated to work satisfactorily in simulation. The evolved designs are found to be competitive in a human environment and are also demonstrated to work in a laboratory set up.

This paper addresses and reports the construction of a reconfigurable logic block that can morph between all three input, one output logic functions based on chaos computing theory. The logic block is constructed based on a discrete chaotic circuit and can emulate all three input, one output logic functions. We have derived instruction set table of this logic block from the block that can be used as a look up table to generate any special three input, one output logic function. Additionally, sensitivity of constructed logic block to noise is investigated and a method for enhancing robustness of block with respect to the environment noise is proposed and implemented. This chaotic block offers inventive approaches for constructing higher order logic functions.

A four-dimensional continuous-time autonomous hyperchaotic system is proposed in this letter. This system is constructed by incorporating a nonlinear control to a three-dimensional continuous-time autonomous chaotic system. The hyperchaotic system is analyzed by studying the spectrum of Lyapunov exponents and the corresponding bifurcation diagram. The system exhibits chaotic, periodic, hyperchaotic behaviors for different values of a selected control parameter. Also, a simple electronic circuit is designed and implemented. Simulations and experimental observations verify the analytical results.

This paper provides a practical implementation of a memristor based chaotic circuit. We realize a memristor using off-the-shelf components and then construct the memristor along with the associated chaotic circuit on a breadboard. The goal is to construct a physical chaotic circuit that employs the four fundamental circuit elements — the resistor, capacitor, inductor and the memristor. The central concept behind the memristor circuit is to use an analog integrator to obtain the electric flux across the memristor and then use the flux to obtain the memristor's characterstic function.

This paper presents a simple scheme for designing mixed-mode chaotic circuits using quadrature core oscillators. Two mixed-mode circuits are constructed by using a few operational amplifiers in suitable combination with some autonomous/nonautonomous second/third-order chaotic circuits. Simulation and experimental results have verified the simplicity and effectiveness of the new design.

We propose a very simple implementation of a second-order nonautonomous chaotic oscillator, using a threshold controller as the only source of nonlinearity. We demonstrate the efficacy and simplicity of our design through numerical and experimental results. Further, we show that this approach of using a threshold controller as a nonlinear element, can be extended to obtain autonomous and multiscroll chaotic attractor circuits as well.

A chaotic attractor has been observed with an autonomous circuit that uses only two energy-storage elements: a linear passive inductor and a linear passive capacitor. The other element is a nonlinear active memristor. Hence, the circuit has only three circuit elements in series. We discuss this circuit topology, show several attractors and illustrate local activity via the memristor's DC v_M - i_M characteristic.

Quasiperiodically forced series LCR circuit with simple nonlinear element is studied analytically and experimentally. To the best of our knowledge, this is the first time that strange nonchaotic attractors (SNAs) are studied analytically. From the explicit analytical solution, the bifurcation process is shown. With a single negative conduction region of the nonlinear element two routes namely, Heagy–Hammel and fractalization routes to the birth of SNA are identified. The analytical analysis are confirmed by laboratory hardware experiments. In addition, for the first time, a detailed stroboscopic Poincaré map is generated experimentally for two different frequencies, for the above two routes, which clearly confirm the presence of SNAs in these two routes. Also, from the experimental data of the corresponding attractors, we quantitatively confirm the presence of SNAs through singular-continuous spectrum analysis. The analytical results as well as experimental observations are characterized qualitatively in terms of phase portraits, Poincaré map, power spectrum, and sensitivity dependance on initial conditions.

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage–current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost.

In this paper, a physical SBT memristor-based chaotic circuit is presented. The circuit dynamic behavior of dependence on the initial state of the SBT memristor and a key circuit parameter are investigated by theoretical analyses and numerical simulations. The results indicate that different initial states of the SBT memristor and the key circuit parameter can significantly impact the dynamic behavior of the chaotic circuit, such as stable sink, periodic cycle, chaos, and even some complex transient dynamics. It can guide future research on the realization of chaotic circuit based on physical SBT memristor.