Shil'nikov Chaos control using Homoclinic orbits and the Newhouse region

A method of controlling Shil'nikov's type chaos using windows that appear in the 1 dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and applied to the electronic Chua's circuit. A demonstration of the chaos control in the electronic circuit experiments and their simulations and bifurcation analyses are given.Comment: 23 pages, 48 figure

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

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

CHAOS SYNCHRONIZATION USING SUPER-TWISTING SLIDING MODE CONTROL APPLIED ON CHUA’S CIRCUIT

Chua’s circuit is the classic chaotic system and the most widely used in serval areas due to its potential for secure communication. However, developing an accurate chaos control strategy is one of the most challenging works for Chua’s circuit. This study proposes a new application of super twisting algorithm (STC) based on sliding mode control (SMC) to eliminate or synchronize the chaos behavior in the circuit. Therefore, the proposed control strategy is robust against uncertainty and effectively regulates the system with a good regulation tracking task. Using the Lyapunov stability, the property of asymptotical stability is verified. The whole of the system including the (control strategy, and Chua’s circuit) is implemented under a suitable test setup based on dSpace1104 to validate the effectiveness of our proposed control scheme. The experimental results show that the proposed control method can effectively eliminate or synchronize the chaos in the Chua's circuit

Simple 4d – Hyperchaotic Canonical Van der pol Duffing Oscillator using Current Feedback Op-Amp

In this paper, in order to show some interesting phenomena of fourth-order hyperchaotic Canonical Van der Pol Duffing oscillator circuit with a smooth cubic nonlinearity, different kinds of attractors, time waveforms and corresponding Lyapunov exponent spectra of systems are presented, respectively. The perturbation transforms an unpredictable hyperchaotic behavior into a predictable hyperchaotic or periodic motion via stabilization of unstable, aperiodic, or periodic orbits of the strange hyperchaotic attractor. One advantage of the method is its robustness against noise. A theoretical analysis of the circuit equations is presented, along with experimental simulation and numerical results

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

New realization of Chua's circuit and verification of chaos by harmonic balance analysis

Chua's circuit, which consists of two capacitors, one inductor, two resistors, one linear voltage-controlled voltage source (VCVS) and voltage-controlled current source (VCCS) type non-linear element has been realized by operational amplifiers. Various dynamical phenomena such as periodic orbit with periods T, 2T, and 4T, single scroll and double scroll similar to the Lorenz attractor have been observed experimentally by changing only the resistance value of the linear resistor R6. The experimental observations have been confirmed by computer simulations and also using harmonic balance analysis