Hiroyuki Asahara, Takuji Kousaka, Tetsushi Ueta, Analysis of bifurcation in oscillatory circuits, Oscillator Circuits: Frontiers in Design, Analysis and Applications, Y. Nishio (ed.)Inspec/Iee, 5-24, London, Dec. 2016.
Abstract: In this chapter, we investigate the bifurcation phenomena observed in oscillatory circuits. The stability and bifurcation phenomena in autonomous systems are introduced by focusing on the equilibrium point and the fixed point. The characteristics and conditions of the saddlenode bifurcation, Hopf bifurcation, and pitchfork bifurcation are discussed for the equilibrium point. Likewise, the characteristics and conditions of the saddle-node bifurcation, period-doubling bifurcation, Neimark Sacker bifurcation, and pitchfork bifurcation are introduced for the fixed point. The method for computing the bifurcation points of the equilibrium point and the periodic points is also introduced, and an example of an application is presented.