Experimental realization of strange nonchaotic attractors in a nonlinear series LCR circuit with nonsinusoidal force

Abstract

We have identified several prominent routes, namely, fractalization, fractalization followed by intermittency, intermittency and Heagy-Hammel routes, for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system with nonsinusoidal (square wave) force as one of the quasiperiodic forces [Senthilkumar et al., 2008]. In addition, a new bubbling route has also been identified in this circuit. Although some of these prominent routes have been reported experimentally [Thamilmaran et al., 2006] in a quasiperiodically forced electronic circuit with both the forcings as sinusoidal forces, experimental identification of all these routes is reported here in a quasiperiodically forced electronic circuit with one of the forcings as a nonsinusoidal (square wave) force. The birth of SNAs by these routes are characterized from both the experimental and numerical data by the maximal Lyapunov exponents and their variance, Poincare maps, Fourier amplitude spectra, spectral distribution functions and the distribution of finite-time Lyapunov exponents.