  The role of the number of breakpoints $N$ in the sawtooth form of the
characteristic function in the modified Chua's circuit model equation on
vibrational and ghost-vibrational resonances is investigated in this paper. To
observe vibrational resonance the system should be driven by two periodic
forces of frequencies $\omega$ and $\Omega$, with $\Omega\gg\omega$. Resonance
occurs at the frequency $\omega$ when the amplitude of the high-frequency force
is varied. When the system is subjected to an input signal containing
multi-frequencies which are higher-order of a certain (missing) fundamental
frequency, then a resonance at the missing fundamental frequency is induced by
the high-frequency input signal and is called ghost-vibrational resonance. In
both types of resonances, the number of resonances is $N$ and hysteresis occurs
in each resonance region. There are some similarities and differences in these
two resonance phenomena. We report in detail the influence of the role of
number of breakpoints $N$ on the features of vibrational and ghost-vibrational
resonances.
