  The equation of the Van der Pol oscillator, being characterized by a
dissipative term, is non-Lagrangian. Appending an additional degree of freedom
we bring the equation in the frame of action principle and thus introduce a
one-way coupled system. As with the Van der Pol oscillator, the coupled system
also involves only one parameter that controls the dynamics. The response
system is described by a linear differential equation coupled nonlinearly to
the drive system. In the linear approximation the equations of our coupled
system coincide with those of the Bateman dual system (a pair of damped and
anti-damped harmonic oscillators). The critical point of damped and anti-damped
oscillators are stable and unstable for all physical values of the frictional
coefficient $\mu$. Contrarily, the critical points of the drive- (Van der Pol)
and response systems depend crucially on the values of $\mu$. These points are
unstable for $\mu > 0$ while the critical point of the drive system is stable
and that of the response system is unstable for $\mu < 0$. The one-way coupled
system exhibits bifurcations which are different from those of the uncoupled
Van der Pol oscillator. Our system is chaotic and we observe phase
synchronization in the regime of dynamic chaos only for small values of $\mu$.
