Analytical Study and Experimental Confirmation of SNA Through Poincare Maps in a Quasiperiodically Forced Electronic Circuit

作者：Arulgnanam A^*; Prasad Awadesh; Thamilmaran K; Daniel M

来源：International Journal of Bifurcation and Chaos, 2015, 25(8): 1530020.

DOI：10.1142/S0218127415300207

• SNA
• Heagy-Hammel
• fractalization
• chaotic circuit
• stroboscopic Poincare maps
• simple nonlinear element and singular-continuous spectrum

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 Poincare 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, Poincare map, power spectrum, and sensitivity dependance on initial conditions.

• 出版日期2015-7