Quasiperiodically forced series LCR circuit with simple nonlinear element is studied analytically and experimentally. To the best of our knowledge, this is the first time that strange nonchaotic attractors (SNAs) are studied analytically. From the explicit analytical solution, the bifurcation process is shown. With a single negative conduction region of the nonlinear element two routes namely, Heagy–Hammel and fractalization routes to the birth of SNA are identified. The analytical analysis are confirmed by laboratory hardware experiments. In addition, for the first time, a detailed stroboscopic Poincaré map is generated experimentally for two different frequencies, for the above two routes, which clearly confirm the presence of SNAs in these two routes. Also, from the experimental data of the corresponding attractors, we quantitatively confirm the presence of SNAs through singular-continuous spectrum analysis. The analytical results as well as experimental observations are characterized qualitatively in terms of phase portraits, Poincaré map, power spectrum, and sensitivity dependance on initial conditions.
Probabilistic inference of bifurcations in single-cell data using a hierarchical mixture of factor analysers
