  A simple electronic circuit with a voltage controlled current source is
investigated. The circuit exhibits rich dynamics upon varying the circuit
elements such as L,C and R, and the control factor of the current source. Among
several other interesting features, the circuit demonstrates two local
bifurcations, namely, node to spiral and Hopf bifurcation, and a global
homoclinic bifurcation. Phase-portraits corresponding to these bifurcations are
presented and the implications of these bifurcations on system stability are
discussed. In particular, the circuit parameters corresponding to the onset of
Hopf bifurcation may be exploited to design an oscillator with stable frequency
and amplitude. The circuit may be easily implemented with nonlinear resistive
elements such as diodes or transistors in saturation and a gyrator block as the
voltage controlled current source.
