An inductor-free realization of the Chua’s circuit based on electronic analogy

Although literature presents several alternatives, an approach based on the electronic analogy was still not considered for the implementation of an inductor-free realization of the double scroll Chua’s circuit. This paper presents a new inductor-free configuration of the Chua’s circuit based on the electronic analogy. This proposal results in a versatile and functional inductorless implementation of the Chua’s circuit that offers new and interesting features for several applications. The analogous circuit is implemented and used to perform an experimental mapping of a large variety of attractors.     

Hyperchaos in SC-CNN based modified canonical Chua’s circuit

In this paper, a state-controlled cellular neural network (SC-CNN)-based hyperchaotic circuit is implemented for classical modified canonical Chua’s circuit. The proposed system is modeled by using a suitable connection of four state-controlled generalized CNN cells, while the stability of the circuit is studied by determining the eigenvalues of the stability matrices, the system parameter is varied, and the dynamics as well as the onset of chaos and hyperchaos followed by a period-three doubling bifurcation has been studied through numerical analysis of the generalized SC-CNN equations and real-time experiments. We further validate our findings, the chaotic and hyperchaotic dynamics, characterized by two positive Lyapunov exponents and Lyapunov dimension, is described by a set of four coupled first-order generalized SC-CNN equations. This has been investigated extensively not only analyzing by computer simulation but also demonstrating by laboratory experiments. The experimental results such as phase portraits, Poincaré surface sections and power spectra are in good agreement with those of numerical computations.     

An experimental study on SC-CNN based canonical Chua’s circuit

In this paper, a State Controlled Cellular Neural Network (SC-CNN) based autonomous canonical Chua’s circuit is presented. The proposed system is modeled by using suitable connection of three simple state controlled generalized CNN cells. The stability of the circuit is studied by determining the eigenvalues of the stability matrices, while the dynamics as well as onset of chaos have been studied through real time experiments and numerical analysis of the generalized SC-CNN equations. The experimental results such as phase portraits and power spectra are in good agreement with those of numerical computations.     

Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics

This paper presents a theoretical stability analysis of a memristive oscillator derived from Chua’s circuit in order to identify its different dynamics, which are mapped in parameter spaces. Since this oscillator can be represented as a nonlinear feedback system, its stability is analyzed using the method based on describing functions, which allows to predict fixed points, periodic orbits, hidden dynamics, routes to chaos, and unstable states. Bifurcation diagrams and attractors obtained from numerical simulations corroborate theoretical predictions, confirming the coexistence of multiple dynamics in the operation of this oscillator.     

On hidden twin attractors and bifurcation in the Chua’s circuit

Recently a new attractor, called hidden attractor, has been found in the well-known Chua’s circuit, whose basin of attraction does not contain neighborhood of any equilibrium. This paper will restudy this circuit, showing that two hidden attractors can coexist in this circuit for some parameters, and characterizes the basins of these two attractors by means of computer method as well. In addition, a computer-assisted proof of the chaoticity of these attracters is presented by a topological horseshoe theory.     

Chaos synchronization and transmission of information in coupled SC-CNN-based canonical Chua’s circuit

In this paper, an experimental implementation of State Controlled Cellular Neural Network (SC-CNN)-based canonical Chua’s circuit is presented. Two such electronic circuits are realized. One of the circuits is configured as driver or transmitter, and other circuit is configured as response or receiver system. Synchronization of chaos between the driver and the driven system is demonstrated. The conditions under which complete synchronization is ensured are derived by applying a strategy based on the Master Stability Function and Lyapunov function. We show that transmitter and receiver systems consisting of cascaded SC-CNN-based canonical Chua’s oscillator can synchronize when they are coupled using direct information from the transmitter into the receiver. The communication performances of different information signals such as sinusoidal, square, and speech signals are demonstrated by real-time hardware experiments. The experimentally observed results are in agreement with the numerically obtained results, and they closely match with each other.     

Periodicity detection on the parameter-space of a forced Chua’s circuit

We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua’s circuit with the aim to build the Periodicity-parameter-space (P-parameter-space). As results of the P-parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work.     

Multistability induced by two symmetric stable node-foci in modified canonical Chua’s circuit

This paper proposes a modified canonical Chua’s circuit using an one-stage op-amp-based negative impedance converter and an anti-parallel diode pair. Unlike the conventional Chua’s circuit, this modified canonical Chua’s circuit has one unstable zero node-focus and two stable nonzero node-foci, but complex dynamical behaviors including period, chaos, stable point, and coexisting bifurcation modes are numerically revealed and experimentally verified. Up to six kinds of coexisting multiple attractors, i.e., left-right limit cycles, left-right chaotic spiral attractors and left-right point attractors, are numerically depicted and physically captured. Furthermore, with dimensionless Chua’s equations, dynamical properties of the Chua’s system are investigated, and two symmetric stable nonzero node-foci are validated to exist in the selected parameter regions thus resulting in the emergence of multistability. Specially, multistability with six different steady states is revealed in a narrow parameter range. Within this parameter region, three bifurcation routes are displayed under different initial conditions, and three sets of topologically different and disconnected attractors are observed.     

Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior

This paper presents an experimental characterization of the behavior of an analogous version of the Chua’s circuit. The electronic circuit signals are captured using a data acquisition board (DAQ) and processed using LabVIEW environment. The following aspects of the time series analysis are analyzed: time waveforms, phase portraits, frequency spectra, Poincaré sections, and bifurcation diagram. The circuit behavior is experimentally mapped with the parameter variations, where are identified equilibrium points, periodic and chaotic attractors, and bifurcations. These analysis techniques are performed in real-time and can be applied to characterize, with precision, several nonlinear systems.     

Hopf bifurcation and hidden attractor of a modified Chua’s equation

Nonlinear Dynamics - We made an attempt to provide a realistic picture of the localization of energy in microtubules (MTs), and we intend to model the nonlinear dynamics of MTs using the...     

Strain Incompatibility in Single Crystals: Kröner’s Formula Revisited

In this paper we prove under precise working assumptions a famous relation originally due to Ekkehart Kröner (Physiques des défauts, Les Houches session XXXV, 1980) relating linear elastic strain incompatibility and dislocation and disclination densities. The 3D case with a set of isolated skew (skew lines are lines which do not intersect but are not parallel either) defect lines in a single crystal is considered according to a mathematical approach taking into account the combined effects of field multivaluedness and concentration properties.     

A new type of stone dome based on Abeille’s bond

We deal with a new kind of stone spherical vaults, bonded adapting Joseph Abeille’s 1699 patent for flat vaults. After the presentation of a parametric design procedure, we put forward a numerical model and propose a method to seek the optimal parameters. We conclude giving tools to process the information and produce fabrication outputs.Most of the issues related to the stereotomy of the quoted system are solved; the automatic design of such vaults is made accessible starting from the choice of a topology and a few geometric parameters. A finite element model of the structure is put forward, sufficiently rich to nourish with numerical results the seek of optimality. A graphic representation of such results is proposed to characterize synthetically each structure’s performances and compare tentatives to select the optimum.Examples are given of optimal choices of the design parameters.     

Minimum-time optimal control of robotic manipulators based on Hamel’s integrators

Meccanica - In this paper, we develop a framework of time optimization path planning for robotic manipulators surrounded by static obstacles. Our approach is based on the recursive dynamics method...     

On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors

Nonlinear Dynamics - Chua’s circuit is one of the well-known nonlinear circuits which have been used to study a rich variety of nonlinear dynamic behaviors such as bifurcation, chaos, and...