Algebraically computable piecewise linear nodal oscillators

A family of piecewise linear oscillators whose oscillation can be completely characterized by algebraic methods is studied. It represents up to the best of authors’s knowledge, the first planar example where all the oscillation properties can be determined for all the values of the bifurcation parameter. In fact, algebraic expressions for coordinates of representative points, period and characteristic multiplier of the corresponding periodic orbit are provided. Thus, the studied family of oscillators deserves to be considered a good benchmark for testing approximate methods of analysis in nonlinear oscillation theory.The piecewise linear oscillators studied are called nodal oscillators, since their relevant linear parts are of node type, and they are not perturbations of the harmonic oscillator. They represent real models in practice, as it is shown for an electronic circuit modeling a piecewise linear version of the classical Van der Pol oscillator.