A Single-Node Classifier Implementation on Chua Oscillator within a Physical Reservoir Computing Framework

The study lies in the field of physical reservoir computing and aims to develop a classifier using Fisher Iris dataset for benchmark tasks. Single Chua chaotic oscillator acts as a physical reservoir. The study was performed using computer simulation. The features of Iris flowers are represented as the consequence of short pulses at a constant level of a control parameter, which is fed to the oscillator, changing its dynamics. During the classification of flowers, the oscillator works without being reset, so each pulse on the input changes the phase trajectory and makes it unique for each Iris flower. Finally, the estimation of the symmetry of an attractor makes it possible to connect each species of Iris with the properties of the attractor. The resulting architecture of the classifier includes a single-node externally-driven Chua oscillator with time-delayed input. The classifier shows two mistakes in classifying the dataset with 75 samples working in chaotic mode.

Robust Control Methods for Finite Time Synchronization of Uncertain Nonlinear Systems

This chapter addresses the dynamic analysis and two different control strategies for the synchronization of new topology of Colpitts oscillator submitted to uncertainties and external disturbances. The diagrams obtained reveal precisely spirals bifurcation and chaos when for a specific values of the system parameters. Based on the relevant control, the authors have controlled this striking phenomenon in the system. The first (control) deals with the sliding mode control (SMC) method. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. The second presents an adaptive robust tracking control strategy based on a modified polynomial observer which tends to follow exponentially the chaotic Colpitts circuits brought back to a topology of the Chua oscillator with perturbations. To highlight the contribution, they also present some simulation results with the purpose to compare the proposed method to the classical polynomial observer.

Sliding Bifurcations in the Memristive Murali–Lakshmanan–Chua Circuit and the Memristive Driven Chua Oscillator

In this paper, we report the occurrence of sliding bifurcations admitted by the memristive Murali–Lakshmanan–Chua circuit [Ishaq & Lakshmanan, 2013] and the memristive driven Chua oscillator [Ishaq et al., 2011]. Both of these circuits have a flux-controlled active memristor designed by the authors in 2011, as their nonlinear element. The three-segment piecewise-linear characteristic of this memristor bestows on the circuits two discontinuity boundaries, dividing their phase spaces into three subregions. For proper choice of parameters, these circuits take on a degree of smoothness equal to one at each of their two discontinuities, thereby causing them to behave as Filippov systems. Sliding bifurcations, which are characteristic of Filippov systems, arise when the periodic orbits in each of the subregions, interact with the discontinuity boundaries, giving rise to many interesting dynamical phenomena. The numerical simulations are carried out after incorporating proper zero time discontinuity mapping (ZDM) corrections. These are found to agree well with the experimental observations which we report here appropriately.

Compositing Coexisting Attractors by Linear Augmentation

In this paper, the composition of coexisting attractors is achieved through the control method of linear augmentation, which can also be considered as a new idea to generate multiscroll attractors. In order to prove the effectiveness, Chua oscillator and classical Lorenz system are taken into consideration. Furthermore, the corresponding electronic circuit is designed based on Lorenz system. The multism simulation results and the hardware experimental results are in agreement with the numerical simulations on the matlab platform, which verifies the feasibility of this control method.

EMI Reduction in Low Input Ripple DC-DC Converter using Chaos PWM technique

This paper presents a chaotic PWM switching technique for a high boost DC-DC converter with a very low ripple at the input current. The use of a choatic PWM allows a reduction of Electromagnetic In (EMI) at the output of power converters by spreading the energy spectrum of the output voltage. In this paper a chaotic PWM, using the Chua oscillator, has been implemented in Matlab for the converter under study and a comparison with a traditional PWM control has been done. A detailed description of the generation of the chaotic carrier is presented and the effect on the output EMI mitigation has been shown.

Global asymptotic synchronization of a class of non-linear systems via sampled-data feedback

In this paper, we investigate the problem of using sampled-data feedback to synchronize a slave (driven) system with a master (driver) system. Based on the domination approach, both state-feedback and output-feedback control methods using sampled-data are proposed to make the tracking error converge to zero. The problem is of practical importance since in practice the system state is transmitted as sampled signal, and very often only the output is measurable. The effectiveness of the proposed approach is illustrated by the simulation for a chaotic Chua oscillator.

Chaotic Synchronization of a Class of Nonlinear Systems via Sampled-Data State Feedback

This paper presents a control strategy for the problem of using sampled-data feedback to synchronize a slave chaotic system with a master chaotic system. The problem is of practical importance since in practice the system states is transmitted as a sampled signal. In order to solve this problem, a sampled-data controller using state feedback is designed to make the tracking error converge to zero. An application to a chaotic Chua oscillator illustrates the effectiveness of the proposed approach.

AN UNIVERSAL PHENOMENON IN MUTUALLY COUPLED CHUA'S CIRCUIT FAMILY

This paper presents the universality of the coexistence of complete synchronization with the recently new proposed inverse π-lag synchronization, in the case of mutually coupled systems of Chua's circuit family. The phenomenon of multistability and the nature of this circuit family systems are the key-points which lead to the explanation of this coexistence. For the need of this work, the most representative circuit of this circuits' family, the Chua oscillator, is used. Simulation results confirm this universality in the class of Chua's circuit family.

A PARAMETER-SPACE OF A CHUA SYSTEM WITH A SMOOTH NONLINEARITY

In this paper we investigate, via numerical simulations, the parameter space of the set of autonomous differential equations of a Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode was replaced by a cubic polynomial. As far as we know, we are the first to report that this parameter-space presents islands of periodicity embedded in a sea of chaos, scenario typically observed only in discrete-time models until recently. We show that these islands are self-similar, and organize themselves in period-adding bifurcation cascades.