  A van der Pol self sustained oscillator with higher order nonlinearity
exhibits a rich dynamics, with multiple periodic attractors, and still the
model allows analytical approximations. Some of these properties can be
conveniently exploited in the framework of circadian oscillations. When
interpreted as a biological oscillator that determines the alternation
sleep/awake, the dynamic variable exhibits some interesting features that can
be related to biological behavior. We analyze in the paper the phenomenon of
entrainment of van der Pol-type circadian pacemaker to daylight cycle. We
determine the amplitude and frequency of the circadian model without natural
forcing light, and find that the agreement of between analytical and numerical
results hardly depend on the stiffness coefficient, $ \mu $ of circadian
oscillations. It is shown that a practical and precise drive which imitates the
effects of the conditions of natural light can be introduced in the system and
analytically treated. Considering the effects of forcing light on the sleep
aware cycle model, we find that a strong drive destroys the circadian
oscillations and thus we confirm the importance of darkness for regular
circadian oscillations. Moreover, we observe the reverse situation when we take
into account the phase in the forcing light. For instance, for $\phi = \pi/2$
and the duration of daylight $D_L = 12h$, the phenomenon of quenching of
circadian oscillations disappears. The comparison between analytical treatment
and numerical simulations of effects of light is discussed.
