Relaxation Oscillators with Exact Limit Cycles

As an inverse problem for relaxation oscillators modeled by the autonomous Li´enard differential equation, we assume plausible exact expressions for the limit cycles in the phase plane which correspond to periodic solutions.toward which all solutions converge, or from which they recede, as time tends to infinity. We illustrate this by two examples, one of which concerns an approximation to a Van der Pol oscillator. The results could be utilized for the synthesis problem, i.e., the construction of oscillator circuits yielding desired periodic behavior.