Parameter space of experimental chaotic circuits with high-precision control parameters

Abstract

We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.

Exploring an experimental analog Chua’s circuit

“…The reason for this is due to experimental characteristics of the nonlinearity i D of Figure 1 (green box). As reported elsewhere [23,37], the discontinuities of the experimental piecewise linear i D curve become rounded and asymmetric, so that a cubic function fits better.…”

“…However, there is a lack of analytical results to corroborate these numerical results. On the other hand, until now few experimental works have reported results of these complex structures on the parameter planes of dynamical systems [10,[22][23][24][25][26], mainly due to the experimental a e-mail: mbeims@fisica.ufpr.br difficulties in varying simultaneously two control parameters of the system and intrinsic noise that distorts results from the theoretical previsions.…”

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

“…We show the results applying numerical methods and analytical analysis. The numerical methods are based on the iteration of the map and obtain the two-dimensional diagrams for the largest Lyapunov exponent (Lyapunov diagram) [9,18,19,20] (see also references therein), and for the periods of the attractors (isoperiodic diagram) [21,22,23,24] as two parameters of the studied map are varied. The Lyapunov diagrams were obtained combining the set of parameters K, γ, β taken two by two with the largest Lyapunov exponent being evaluated as the map is iterated.…”

Stability diagrams for a memristor oscillator

“…A search for such behaviors demands considerable additional investment of computer time and, therefore, is not further pursued here. It is hoped that the rich predictions of an organized unfolding of oscillations discovered in the present prospection may motivate their experimental investigation, along the lines recently done for a Duffing-like proxy designed to bypass noisy spectra conspicuously present in oscillators [33], in the standard circuit of Chua [34], and in other scenarios [35,36].…”