The independent coordinate  has sense of time. Indeed, it may be proportional to time  with some relation like , where  is constant.
The derivative  may have sense of velocity of particle with coordinate ; then  can be interpreted as acceleration; and the mass of such a particle is equal to unity.
The dissipative function  may have sense of coefficient of the speed-proportional friction.
Usually, both parameters  and  are supposed to be positive; then this speed-proportional friction coefficient grows exponentially at large positive values of coordinate .
The potential  is a fixed function, which also shows exponential growth at large positive values of coordinate .
In the application in laser physics,  may have a sense of logarithm of number of photons in the laser cavity, related to its steady-state value.  Then, the output power of such a laser is proportional to  and may show pulsation at oscillation of .
Both analogies, with a unity mass particle and logarithm of number of photons, are useful in the analysis of behavior of the Toda oscillator.