Ferroelectrics Nonlinearity to Realize Chaotic Circuits.

In this paper the possibility of observing chaotic behaviour in an electronic circuit including a nonlinear ferroelectrics has been investigated. The ferroelectrics constitutes the medium interposed between the two plates of a capacitor, and is obtained by successive vapour deposition of Strontium, Tantalum and Bismuth on Platinum substrates in small areas. The device is characterized by a nonlinear hysteretic behaviour observed by estimating the output voltage by using a Sawyer-Tower configuration. Different circuits showing chaos and based on hysteretic behaviour of the nonlinearities have been reported in literature. In particular, in the circuit reported in [1] the nonlinearity consists of a piecewise linear resistor, only the two tracts with positive slope are effectively involved in the dynamics and an hysteretic behaviour switching between these two linear segments of the nonlinearity can be addressed as responsible of the emergence of iperchaos in the circuit. Starting from the chaos generator reported in [1], the following dimensionless equations have been developed: where f(x) is the nonlinearity due to the hysteresis of the ferroelectrics capacitor. The functional f(x) constitutes a simple model of the ferroelectrics device and is defined by two functions (the upper curve and the lower curve based on experimental data on the ferroelectrics). Chaotic solutions of system (1) were searched for, by performing numerical integration with respect to different values of the parameters. Finally, the circuit implementing equations (1) has been realized. Experimental results show that for a suitable range of parameter a chaotic attractor emerges. Fig. 1 shows the projection of the attractor onto the phase plane x1-x2. The paper addresses the possibility of exploiting the rich dynamics of ferroelectrics hysteresis to obtain new chaotic attractors with low cost circuits. © 2003 American Institute of Physics [ABSTRACT FROM AUTHOR]