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

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.

Characterization of a sulfonated polycarbonate resistive humidity sensor.

In this work; resistive moisture sensors were obtained by dip coating sulfonated polycarbonate (SPC) onto silver interdigitated electrodes. Commercial polycarbonate was sulfonated with acetyl sulphate at two different sulfonation degrees corresponding to 9.0 and 18.0 mole %. Impedance spectroscopy was used to investigate the humidity sensing properties at controlled relative humidity (RH%) environments generated from standard saline solutions in the range of 11-90 RH%. For the highest sulfonated sample; in the RH% range investigated (11 to 90%); the sensor impedance changed from 4.7 MΩ to 18 kΩ. Humidity sensors made from sulfonated polycarbonate showed exponential decay behavior of the impedance at constant frequency with the environmental relative humidity. Sample 9SPC presented dielectric relaxation response for environmental humidity between 58 and 90 RH% while sample 18SPC presented dielectric relaxation response for the entire measured range between 11 and 90 RH%. Sulfonated polycarbonate could be a promising material for the fabrication of simple and cheap humidity-sensing sensors for the assessment of relative humidity of the surrounding environment, as suggested by experimental results.

Lyapunov exponent diagrams of a 4-dimensional Chua system.

We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.

High-resolution parameter space of an experimental chaotic circuit.

A high-resolution codimension-two parameter space showing the abundance of complex periodic structures of an experimental chaotic circuit is reported. Such resolution was propitiated by the use of a 0.5 mV step dc voltage source as one of the control parameters. Those complex periodic structures organize themselves in a period-adding bifurcation cascade that accumulates in a chaotic region. Numerical investigations on the dynamical model were also carried out to corroborate several new features observed in the experimental high-resolution parameter space.

Mutual information rate and bounds for it.

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.