= Softening Rayleigh-Duffing oscillator
{title2=$z''+z=-Az'+z^3-(z')^3$}
The softening restoring force and cubic velocity damping give the energy $E=(z')^2/2+z^2/2-z^4/4$ with $\dot E=-A(z')^2-(z')^4$. The origin and the two saddle points $z=\pm1$ persist for all parameters. The origin undergoes a <supercritical Hopf bifurcation> at $A=0$. A <heteroclinic cycle> and a subsequent <saddle-node bifurcation of periodic orbits> are distinct global changes in its <softening Rayleigh-Duffing phase portrait>.
Back to article page
