a simple circuit model showing feature-rich Bogdanov-Takens bifurcation

A circuit model is proposed for studying the global behavior of the normal form describing the Bogdanov-Takens bifurcation, which is encountered in the study of autonomous dynamical systems arising in different branches of science and engineering. The circuit is easy-to-implement and one can experimentally study the rich dynamics and bifurcations simply by altering the values of some linear circuit elements (R, L, C) and the e.m.f. of a d.c. voltage source. It is shown that the system exhibits three local (saddle-node, Andronov-Hopf, spiral-to-node) bifurcations and one global (Homoclinic) bifurcation. The phase portraits associated with each of these bifurcations are presented, which serve to illustrate the qualitative changes in the system’s dynamics across a bifurcation curve. The implications of these changes on the system’s stability are discussed.