  The behaviour of a space-modulated, so-called "argumental" oscillator is
studied, which is represented by a model having an even-parity space-modulating
function. Analytic expressions of a stability criterion and of discrete energy
levels are given. Using an integrating factor and a Van der Pol representation
in the (amplitude, phase) space, an approximate implicit closed-form of the
solution is given. The probability to enter a stable-oscillation regime from
given initial conditions is calculated in symbolic form. These results allow an
analytic approach to stability and bifurcations of the system. They also allow
an assessment of the risk of occurrence of sustained large-amplitude
oscillations, when the phenomenon is to be avoided, and an assessment of the
conditions to apply to obtain oscillations whenever the phenomenon is desired.
