Bifurcation and fractal basin boundaries of phase-locked loop circuits

By drawing exact bifurcation diagrams, it is confirmed that the Melnikov curve of homoclinicity gives a good prediction for the onset of the chaotic attractor bifurcated from the periodic solution of the second type in some region of the external sinusoidal force. It is also confirmed that the Melnikov's curve becomes an onset of the fractal basin boundary of multiple attractors. This is confirmed by drawing various initial condition planes above and below the curve.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>