A further contribution to the modelling of multi-waveform generators (Q788885)

The authors write: ''The aim of the paper is to generalize previously suggested methods for constructing a large variety of periodic waveform generator models, which can be represented by a unified system model. The new approach supplies an additional variability in the methods, and thus increases significantly the number of periodic waveforms that can be generated by a relatively simple skeleton model.'' What they in fact do is the presentation of the two-dimensional differential equation \[ \dot x=p(x,y)F(y)+\epsilon_ 1[1-\mu V(x,y)]x\quad \dot y=- p(x,y)G(x)+\epsilon_ 2[1-\mu V(x,y)]y \] where \(\epsilon_ 1,\epsilon_ 2,\mu\) are positive parameters, V is defined as \[ V(x,y)=\int^{x}_{0}G(\xi)d\xi +\int^{y}_{0}F(\eta)d\eta \] and F and G satisfy \(G(x)/x>0\) and \(F(y)/y>0\), respectively. The novelty (compared to previously presented equations) is the arbitrary function p(x,y) which accounts for various waveforms (i.e. solutions vs. time) of the uniquely determined limit cycle.