Chaotic attractors based on unstable dissipative systems via third-order differential equation

"In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in R3 based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.

Signal generator based on a chaotic circuit

"This paper is about a signal generator based on Chua´s circuit. It is able to generate chaotic and sinusoidal signals. It can generate other types of waveforms as well. These results are seen in the experiment carried out on the signal generator. Simple hardware like operational amplifiers along with passive components such as resistors and capacitors are used to make the signal generator.

Difference map and its electronic circuit realization

"In this paper we study the dynamical behavior of the one-dimensional discrete-time system, the so-called iterated map. Namely, a bimodal quadratic map is introduced which is obtained as an amplification of the difference between well-known logistic and tent maps. Thus, it is denoted as the so-called difference map. The difference map exhibits a variety of behaviors according to the selection of the bifurcation parameter. The corresponding bifurcations are studied by numerical simulations and experimentally. The stability of the difference map is studied by means of Lyapunov exponent and is proved to be chaotic according to Devaney’s definition of chaos. Later on, a design of the electronic implementation of the difference map is presented. The difference map electronic circuit is built using operational amplifiers, resistors and an analog multiplier. It turns out that this electronic circuit presents fixed points, periodicity, chaos and intermittency that match with high accuracy to the corresponding values predicted theoretically.

Forced synchronization of autonomous dynamical Boolean networks

"We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.

Set-reset flip-flop circuit with a simple output logic

"The equation of the plane (EOP) in analytic geometry is used to build a logic dynamic architecture, i.e., a combination of set-reset flip-flop (SR-FF) and basic logic gates. This is achieved by using two of the variables in the EOP as the input signals of the SR-FF and the remaining variable as the output signal. This theoretical proposal for mixing the SR-FF and the basic logic gates is confirmed experimentally by means of a simple electronic implementation.

Pseudo-random bit generator based on lag time series

"In this paper, we present a pseudo-random bit generator (PRBG) based on two lag time series of the logistic map using positive and negative values in the bifurcation parameter. In order to hidden the map used to build the pseudo-random series we have used a delay in the generation of time series. These new series when they are mapped xn against xn+1 present a cloud of points unrelated to the logistic map. Finally, the pseudo-random sequences have been tested with the suite of NIST giving satisfactory results for use in stream ciphers.

Pseudo-random bit generator based on multi-modal maps

"In this work we present a pseudo-random Bit Generator via unidimensional multi-modal discrete dynamical systems calledk-modal maps. These multi-modal maps are based on the logistic map and are useful to yield pseudo-random sequences with longer period, i.e., in order to attend the problem of periodicity. In addition the pseudo-random sequences generated via multi-modal maps are evaluated with the statistical suite of test from NIST and satisfactory results are obtained when they are used as key stream. Furthermore, we show the impact of using these sequences in a stream cipher resulting in a better encryption quality correlated with the number of modals of the chaotic map. Finally, a statistical security analysis applied to cipher images is given. The proposed algorithm to encrypt is able to resist the chosen-plaintext attack and differential attack because the same set of encryption keys generates a different cipher image every time it is used.

Chua´s circuit and its characterization as a filter

"This article deals with Chuaʼs circuit characterization from the point of view of a filter based on the concept of piecewise linear functions. Furthermore, experiments are developed for teaching electronic systems that can be used for novel filtering concepts. The frequency range in which they are tested is from $20\;{\rm Hz}$ to $20\;{\rm kHz}$, due to the audio spectrum comprised in this frequency range. The node associated with the capacitor and Chuaʼs diode is used as input, and the node for another capacitor and the coil is used as output, thereby establishing one input–output relationship for each system case given by the piecewise linear functions. The experimental result shows that Chuaʼs circuit behaves as a bandpass filter-amplifier, with a maximum frequency around $3\;{\rm kHz}$ and bandwidth between $1.5\;{\rm kHz}$ and $5.5\;{\rm kHz}$. The results presented in this paper can motivate engineering students to pursue applications of novel electrical circuits based on topics that are of potential interest in their future research studies.

A simple electronic circuit realization of the tent map

"We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values.