A study of chaotic motion in electronic circuits

A Study of Chaotic Motion in Electronic Circuits Perhaps the most well known of the properties that characterize chaotic systems is their sensitivity to initial conditions and their complex nonperiodic motion. In this work, Rössler and Lorenz chaotic systems are implemented in electronic circuits to study their chaotic motions. How the stability of an equilibrium point is affected when the control parameter is varied in the Rössler systems is investigated. If two independent chaotic systems are started with the same initial conditions, any arbitrarily small difference in these conditions will grow exponentially in time. As time elapses, the motions of the two systems will be uncorrelated. But, Pecora and Caroll have shown that it is possible to synchronize two chaotic systems. Under the proper conditions as time elapses the state variables of the chaotic transmitter will converge asymptotically to those of the receiver and continue to remain in step with the values of the variables of the chaotic receiver. To see this behavior, two Lorenz systems were built and, using only one variable for drive, synchronization and subsequent chaotic data transmission were demonstrated. Moreover, in this work, the possibility of synchronization and the chaotic data transmission using two drive variables is shown and simulated in a 5 dimensional system. Thus, it is shown that one pair of synchronized chaotic systems is sufficient to transmit two information-bearing signals using two drive variables.Key Words : Chaos, Bifurcation, Synchronization, Chaotic data transmission