A consideration between conditions for oscillation in linear systems and Hopf bifurcation sets in nonlinear systems

摘要

Linear analysis of singular points is very important and convenient to understand dynamical behavior in a given system. In this paper, we show the equivalence among an oscillating condition by phasor method, an design method of a oscillator based on the Barkhausen criterion, and Hopf bifurcation set in a given dynamical system. Obtained conditions may form manifolds (bifurcation curves or stability limits) in the parameter space. This might show a rich variety of their shape. As a demonstrated example, we show some bifurcation phenomena of bifurcation curves found in the extended BVP equation.