Circuito para medição automática de diagramas de bifurcação em osciladores eletrônicos não lineares. (A Circuit for Automatic Measurement of Bifurcation Diagram in Nonlinear Electronic Oscillators)

Rodrigo Augusto Ricco (, Anny Verly (, Gleison Fransoares Vasconcelos Amaral (

1Universidade Federal de Ouro Preto
2Universidade Federal de São João del-Rei

This paper appears in: Revista IEEE América Latina

Publication Date: July 2016
Volume: 14,   Issue: 7 
ISSN: 1548-0992

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.

Index Terms:
Operational Transconductance Amplifiers, Automatic Gain Control, Nonlinear Dynamical Systems, Bifurcation Diagram, Chaotic Systems   

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