Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system constructed using a negative conductance series LCR circuit with a diode both numerically and experimentally. The birth of SNAs by these three routes is verified from both experimental and their corresponding numerical data by maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier amplitude spectrum, spectral distribution function and finite-time Lyapunov exponents. Although these three routes have been identified numerically in different dynamical systems, the experimental observation of all these mechanisms is reported for the first time to our knowledge and that too in a single second order electronic circuit.Comment: 21 figure

Synchronous Behavior of Coupled Systems with Discrete Time

The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincare sectioning procedure applied to the coupled continuous-time systems in the phase synchronization regime. The behavior (previously considered as asynchronous) of the coupled maps that appears when the complete synchronization regime is broken as the coupling parameter decreases, corresponds to the phase synchronization of flow systems, and should be considered as a synchronous regime. A quantitative measure of the degree of synchronism for the interacting systems with discrete time is proposed.Comment: 4 pages, 2 figure

Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven Duffing oscillator

Different mechanisms for the creation of strange nonchaotic attractors (SNAs) are studied in a two-frequency parametrically driven Duffing oscillator. We focus on intermittency transitions in particular, and show that SNAs in this system are created through quasiperiodic saddle-node bifurcations (Type-I intermittency) as well as through a quasiperiodic subharmonic bifurcation (Type-III intermittency). The intermittent attractors are characterized via a number of Lyapunov measures including the behavior of the largest nontrivial Lyapunov exponent and its variance as well as through distributions of finite-time Lyapunov exponents. These attractors are ubiquitous in quasiperiodically driven systems; the regions of occurrence of various SNAs are identified in a phase diagram of the Duffing system.Comment: 24 pages, RevTeX 4, 12 EPS figure