A circuit for automatic measurement of bifurcation diagram in nonlinear electronic oscillators.

Abstract

Experimental bifurcation diagram is very helpful to describe the global behaviour of nonlinear electronic oscillators. The diagram allows insight gain of the oscillators behaviour for a parameter variation. However, when the bifurcation parameter is a resistance, experimental bifurcation diagrams are hard to achieve. In this case, if the potentiometer resistance has been used to change the gain, it is possible to replace the potentiometer by an alternative circuit using operational transconductance amplifier. This kind of circuit is presented in this work and experimental results are provided to piecewise affine Rössler electronic oscillator. The results obtained show a very good matching with the theoretical diagram. Then, if the bifurcation parameter is a resistance, voltage or current, we have implemented a circuit to extract the experimental bifurcation diagram of all nonlinear electronic oscillators.