Pai Chai University, Republic of Korea

Electronic circuits exhibiting chaotic behaviors have attracted much attention for their availability to simple experimental verification of chaos theory. Until now, such nonlinear electronic circuits have been developed as an inductor-resistor-diode circuit, a Chua circuit, and a double scroll circuit, and many nonlinear phenomena studied in theory have been investigated in these circuits. So to find out a new circuit that exhibits rich chaotic behavior is very important not only for experimental verification of chaos theory but also for application of chaos to practical fields like secure communication. For this, we introduce an element, operational amplifier (OP Amp), which generates chaos for itself. An OP Amp is used as one of the most important electronic elements that performs a wide variety of linear functions. In an OP amp, when the inverting terminal is connected with the output terminal through a resistor, and positive input terminal is grounded, the output signal has a phase shift due to the resistance-capacitance lag network within the amplifier. At this time when the total lag network phase shift equals or exceeds 180 degrees, the system is unstable and can generate a periodic signal. Here, when the absolute voltages of the negative and the positive power supplies are much less than 15 Volts and the resistor is zero, a fast OP Amp generates chaotic behaviors. We carry out an experiment by using LF357, and observe various chaotic behaviors according to the power supplies voltages. The bifurcation diagram and the phase diagram exhibit that the system develops to chaos through period doubling bifurcation. And the return maps show the origins of the chaotic behaviors that are type- I and II intermittencies, periodic windows, crisis, etc. All the experimental results well agree with the chaotic behaviors of the logistic map.