I. Raja Mohamed

Design of time delayed chaotic circuit with threshold controller

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

DESIGN OF THRESHOLD CONTROLLER BASED CHAOTIC CIRCUITS

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.

Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua’s circuits without delay

We construct a new RC phase shift network based Chuas circuit, which exhibits a period-doubling bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chuas oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS or CS is demonstrated without using a variable delay line both experimentally and numerically.

Spread-spectrum image encoding and decoding using ergodic chaos

The large-scale proliferation of wireless communications both inside and outside the home-office environment has led to an increased demand for effective and simple spread-spectrum technology - which provides secure digital communication schemes. Now a new chaos based digital communication scheme is proposed by exploiting the ergodic properties of chaotic signals. A novel approach called the mean-value estimation method which is adapted to propose a robust noncoherent demodulator design for a chaos based digital communication scheme. A simple chaos on-off keying method is utilized at the transmitter and it is found that the proposed scheme is robust even in the presence of low signal-to-noise environments. Further, spread spectrum image encoding and decoding simulation results are demonstrated.

CHAOTIC DYNAMICS OF A SIMPLE PARAMETRICALLY DRIVEN DISSIPATIVE CIRCUIT

We introduce a simple parametrically driven dissipative second-order chaotic circuit. In this circuit, one of the circuit parameters is varied by an external periodic control signal. Thus by tuning the parameter values of this circuit, classic period-doubling bifurcation route to chaos is found to occur. The experimentally observed phenomena is further validated through corresponding numerical simulation of the circuit equations. The periodic and chaotic dynamics of this model is further characterized by computing Lyapunov exponents.

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed that when there is a feedback between the central unit (relay unit) and at least one of the outer units, ZLS occurs in the two outer units whereas the central and outer units exhibit inverse phase synchronization (IPS). We find that in the case of mutual coupling configuration ZLS occurs both in periodic and hyperchaotic regimes, while in the subsystem coupling configuration it occurs only in the hyperchaotic regime. Snapshots of the time evolution of outer circuits as observed from the oscilloscope confirm the occurrence of ZLS experimentally. The quality of ZLS is numerically verified by correlation coefficient and similarity function measures. Further, the transition to ZLS is verified from the changes in the largest Lyapunov exponents and the correlation coefficient as a function of the coupling strength. IPS is experimentally confirmed using time series plots and also can be visualized using the concept of localized sets which are also corroborated by numerical simulations. In addition, we have calculated the correlation of probability of recurrence to quantify the phase coherence. We have also analytically derived a sufficient condition for the stability of ZLS using the Krasovskii-Lyapunov theory.

ORDERED AND CHAOTIC PHENOMENA IN TWO COUPLED FORCED LCR OSCILLATORS SHARING A COMMON NONLINEARITY

This paper suggests a simple mechanism of sharing a common nonlinearity among the linear oscillators to exhibit some interesting phenomena. Here, we present fourth-order nonautonomous circuit capab...

Synchronization of Two Chaotic Oscillators Through Threshold Coupling

In this paper, the dynamic modeling of two identical oscillators which are coupled through threshold controller is proposed. Until now, most of the synchronization of chaotic systems found in literature is based on common coupling methods (unidirectional and bidirectional) that attracted the attention of researchers. To strengthen this, the idea illustrated here is to show the effectiveness of a new kind of coupling called threshold controller coupling. Using this, complete and anticipatory synchronization could be achieved. The system used is of second-order non-autonomous type. The coupled system is investigated using MATLAB–Simulink technique. The result shows that based on coupling strength, coupled system is switched among the basic synchronization, viz. lead and complete.

Design of chaotic system with sinusoidally forced threshold controller

In this paper, the ordered and chaotic behaviors of sinusoidally excited threshold controller based second-order non-autonomous system is explored. The advantage of this analog simulation circuit is to make the system to exhibit periodic, quasiperiodic (torus) and chaotic dynamics. The analysis like time series, phase portrait and frequency spectra are revealed to show the variety of dynamics obtained from this system. Moreover, this proposed system is studied experimentally and simulated using Multisim.

Experimental synchronization of threshold coupled chaotic oscillators

In this paper, a new method of achieving anticipatory and complete synchronization through threshold coupling of two threshold controllers based chaotic oscillators is proposed. Until now, most of the synchronization of chaotic systems stated in the literature are based on common coupling methods like unidirectional and bidirectional coupling but rarely, cascaded and delay coupling. In this direction to add on a new kind of coupling known as threshold coupling is employed in this work. This coupled systems exhibit complete (CS) and anticipatory synchronizations (AS) for decreasing coupling resistor value without parameter mismatch and delay line. The proposed circuit is investigated experimentally and circuit behavior is also simulated using Multisim.