Nonlinear Dynamics of Chaotic Attractor of Chua Circuit and Its Application for Secure Communication

The Chua circuit is among the simplest non-linear circuits that shows most complex dynamical behavior, including chaos which exhibits a variety of bifurcation phenomena and attractors. In this paper, Chua attractor's chaotic oscillator, synchronization and masking communication circuits were designed and simulated. The electronic circuit oscilloscope outputs of the realized Chua system is also presented. Simulation and oscilloscope outputs are used to illustrate the accuracy of the designed and realized Chua chaotic oscillator circuits. The Chua system is addressed suitable for chaotic synchronization circuits and chaotic masking communication circuits using Matlab® and MultiSIM® software. Simulation results are used to visualize and illustrate the effectiveness of Chua chaotic system in synchronization and application of secure communication.  Keywords: chua nonlinear circuit, chaotic attractor, chaotic synchronization, secure communication

Fully CMOS Memristor Based Chaotic Circuit

This paper demonstrates the design of a fully CMOS chaotic circuit consisting of only DDCC based memristor and inductance simulator. Our design is composed of these active blocks using CMOS 0.18 µm process technology with symmetric ±1.25 V supply voltages. A new single DDCC+ based topology is used as the inductance simulator. Simulation results verify that the design proposed satisfies both memristor properties and the chaotic behavior of the circuit. Simulations performed illustrate the success of the proposed design for the realization of CMOS based chaotic applications

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.Comment: submitted to EP

CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit

This paper presents design considerations for monolithic implementation of piecewise-linear (PWL) dynamic systems in CMOS technology. Starting from a review of available CMOS circuit primitives and their respective merits and drawbacks, the paper proposes a synthesis approach for PWL dynamic systems, based on state-variable methods, and identifies the associated analog operators. The GmC approach, combining quasi-linear VCCS's, PWL VCCS's, and capacitors is then explored regarding the implementation of these operators. CMOS basic building blocks for the realization of the quasi-linear VCCS's and PWL VCCS's are presented and applied to design a Chua's circuit IC. The influence of GmC parasitics on the performance of dynamic PWL systems is illustrated through this example. Measured chaotic attractors from a Chua's circuit prototype are given. The prototype has been fabricated in a 2.4- mu m double-poly n-well CMOS technology, and occupies 0.35 mm/sup 2/, with a power consumption of 1.6 mW for a +or-2.5-V symmetric supply. Measurements show bifurcation toward a double-scroll Chua's attractor by changing a bias current

Variations of Boundary Surface in Chua’s Circuit

The paper compares the boundary surfaces with help of cross-sections in three projection planes, for the four changes of Chua’s circuit parameters. It is known that due to changing the parameters, the Chua’s circuit can be characterized in addition to a stable limit cycle also by one double scroll chaotic attractor, two single scroll chaotic attractors or other two stable limit cycles. Chua’s circuit can even start working as a binary memory. It is not known yet, how changes in parameters and conseqently in attractors in the circuit will affect the morphology of the boundary surface. The boundary surface separates the double scroll chaotic attractor from the stable limit cycle. In a variation of the parameters presented in this paper the boundary surface will separate even single scroll chaotic attractors from each other. Dividing the state space into regions of attractivity for different attractors, however, remains fundamentally the same

A chaotic jerk system with different types of equilibria and its application in communication system

In this paper, a new jerk system is designed. This system can display different characters of equilibrium points according to the value of its parameters. The proposed nonlinear oscillator can have both self-excited and hidden attractors. Dynamical properties of this system are investigated with the help of eigenvalues of equilibria, Lyapunov exponents' spectrum, and bifurcation diagrams. Also, an electronic circuit implementation is carried out to show the feasibility of this system. As an engineering application of this new chaotic jerk system, a chaotic communication system is realized by correlation delay shift keying. When the results of the communication system are examined, the transmitted information signal is successfully obtained in the receiving unit, and its performance efficiency is investigated in the presence of additive white Gaussian noise

EKF-based dual synchronization of chaotic colpitts circuit and Chua’s circuit

summary:In this paper, dual synchronization of a hybrid system containing a chaotic Colpitts circuit and a Chua’s circuit, connected by an additive white Gaussian noise (AWGN) channel, is studied via numeric simulations. The extended Kalman filter (EKF) is employed as the response system to achieve the dual synchronization. Two methods are proposed and investigated. The first method treats the combination of a Colpitts circuit and a Chua’s circuit as a higher- dimensional system, while the second method considers the Colpitts circuit and Chua’s circuit separately and utilizes the cross-coupling scheme. The simulation results indicate that the proposed methods can effectively achieve and maintain dual synchronization of the hybrid system through an AWGN channel

Secure communication based on indirect coupled synchronization

In this paper, a secure communication system composed of four chaotic oscillators is proposed. Two of these oscillators are unidirectionally coupled and employed as transmitter and receiver. The other two oscillators are indirectly coupled and are employed as keystream generators. The novelty lies in the generation of the same chaotic keystream both in the transmitter and receiver side for encryption and decryption purposes. We show, in particular, that it is possible to synchronize the two keystream generators even though they are not directly coupled. So doing, an estimation of the keystream is obtained allowing decrypting the message. The main feature of the proposed communication scheme is that the keystream cannot be generated with the sole knowledge of the transmitted chaotic signal, hence making it very secure. The performance of the proposed communication scheme is shown via simulation using the Chua and Lorenz oscillators