Holokx A. Albuquerque

Santa Catarina State University | UDESC · Departamento de Física

In this work, we employ simulations to investigate deterministic and stochastic dynamics of a system governed by four coupled nonlinear ordinary differential equations (ODEs) derived from the canonical three-dimensional Chua model, replacing the piecewise nonlinearity with a cubic function. We employed two simulation approaches: (i) using software...

Cover of International Journal of Bifurcation and Chaos, Volume 33, Issue 12.

The three-dimensional Muthuswamy–Chua–Ginoux (MCG) circuit model is a generalization of the paradigmatic canonical Muthuswamy–Chua circuit, where a physical memristor assumes the role of a thermistor, and it is connected in series with a linear passive capacitor, a linear passive inductor, and a nonlinear resistor. The physical memristor presents a...

Single-walled carbon nanotubes (SWCNTs) can undergo arbitrarily large nonlinear deformations without permanent damage to the atomic structure and mechanical properties. The dynamic response observed in curved SWCNTs under externally driven forces has fundamental implications in science and technology. Therefore, it is interesting to study the nonli...

We analyze the existence of chaotic and regular dynamics, transient chaos phenomenon, and multistability in the parameter space of two electrically interacting FitzHugh–Nagumo (FHN) neurons. By using extensive numerical experiments to investigate the particular organization between periodic and chaotic domains in the parameter space, we obtained th...

In this work, we show that the bailout embedding method is responsible for creating different dynamical behaviors and for destroying intrinsic features present in mixed phase spaces of the area-preserving Hamiltonian maps, where the sticking to regular (or resonant) islands degrades chaotic properties. In particular, the base map chosen for the stu...

We investigate the disturbance on the dynamics of a Watt governor system model due to the addition of a harmonic perturbation and a Gaussian noise, by analyzing the numerical results using two distinct methods for the nonlinear dynamics characterization: (i) the well-known Lyapunov spectrum, and (ii) the 0-1 test for chaos. The results clearly show...

Cover of the IJBC journal showing a figure from the paper: Characterizing the Dynamics of the Watt Governor System Under Harmonic Perturbation and Gaussian Noise.

In this work we carry out experimental studies of the paradigmatic Chua’s circuit using an approach of the analog computation instead of performing experiments in the canonical circuit. This means that we have built an electronic circuit that integrates (analog computation), in continuous time, the equations of motion of the canonical Chua’s circui...

The effect of applying an asymmetric periodic continuous-feedback signal F(x), which is a function of voltage x, across one of the capacitors in the classical Chua’s circuit model is examined. We have performed a numerical investigation on the dynamics of the Chua’s circuit model to discuss a procedure of distorting, suppressing and moving attracto...

Cover of the journal IJBC v.28, issue 11 (October 2018).

We study the dynamics and characterize the bifurcation structure of a phase-locked loop (PLL) device modeled by a third-order autonomous differential equation with sinusoidal phase detector. The development of this work was performed using rigorous analysis and numerical experiments. Through theoretical analysis the bifurcation structures related t...

In this Letter we demonstrate that intrinsic inevitable noise effects, existing in realistic experiments with electronic circuits, are properly described theoretically using a Gaussian noise. For this we integrate numerically the equations of motion from the Chua circuit using a fourth-order stochastic Runge–Kutta integrator. Periodic structures in...

In this work we carry out extensive numerical study of a Watt-centrifugal-governor system model, and we also implement an electronic circuit by analog computation to experimentally solve the model. Our numerical results show the existence of self-organized stable periodic structures (SPSs) on parameter-space of the largest Lyapunov exponent and iso...

In this work we carry out extensive numerical study of a Watt centrifugal governor system model, and we also implement an electronic circuit by analog computation to experimentally solve the model. Our numerical results show the existence of self-organized stable periodic structures (SPSs) on parameter-space of the largest Lyapunov exponent and iso...

In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical...

In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical...

The behavior of neuron systems can be modeled by the FitzHugh-Nagumo model, originally consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of three coupled neurons in a network modeled by the FitzHugh-Nag...

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 technologica...

In this work it is shown the dynamical behavior of driven complex variable oscillators on Lyapunov diagrams, through the computation of the Lyapunov exponents spectrum. Here, we consider the largest and the second largest exponents on Lyapunov diagrams to identify regions of chaotic, quasi-periodic and periodic behaviors. In these diagrams we show...

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional a...

Optimal ratchet currents are shown to be directly connected, for all parameters combinations of the ratchet model, to Isoperiodic Stable Structures (ISSs), which are believed to be generic in the parameter spaces of nonlinear dynamical systems. As the ratchet current is more efficient inside the ISSs, which usually are located in preferred directio...

A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both met...

In this letter we investigate, via numerical simulations, the parameter-space of the set of autonomous first-order differential equations of a Chua circuit. We show that this parameter-space presents self-organized periodic structures immersed in a chaotic region, forming a single spiral structure that coils up around a focal point. Additionally, b...

This work reports the existence of Isoperiodic Stable Ratchet Transport Structures in the parameter spaces dissipation versus spatial asymmetry and versus phase of a ratchet model. Such structures were found [Phys. Rev. Lett. 106, 234101 (2011)] in the parameter space dissipation versus amplitude of the ratchet potential and they appear to have gen...

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 con...

This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures, where larger currents are usually observed inside, appear along preferred direction in the parameter space giving a guide to follo...

We report a numerical bifurcation study on the Chua's circuit with parallel resistor. Through the largest Lyapunov exponent, we constructed a two-dimensional parameter space of the model. We also implemented the experimental circuit to show the similarities between the model and the experimental data. With that modification we discuss the effect of...

We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua’s circuit with the aim to build the Periodicity-parameter-space (P-parameter-space). As res...

In this paper we investigate three two-dimensional parameter spaces of a three-parameter set of autonomous differential equations used to model the Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode has been replaced by a cubic polynomial. It is made by using three independent two-dimen...

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 ca...

In this paper, we report a new four-dimensional autonomous hyperchaotic system, constructed from a Chua system where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode has been replaced by a cubic polynomial. Analytical and numerical procedures are conducted to study the dynamical behavior of the proposed new...

We report the existence of complex periodic structures, forming intricate periodic networks, embedded in chaotic regions of bi-dimensional bifurcation diagrams (parameter spaces) of a chaotic circuit model. Such circuit is composed by a negative differential conductivity (NDC) device coupled with a three variable RLC tank circuit. Particularly, we...

In this paper we investigate, via numerical simulations, the parameter space of the set of autonomous differential equations of a Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode was replaced by a cubic polynomial. As far as we know, we are the first to report that this parameter-spac...

In a 2D parameter-space of an inductorless Chua's circuit model, we carried out numerical investigations and observed self-similar stability structures embedded in a sea of chaos, known until recently just in discrete-time models, namely, shrimps. We showed that those structures are self-similar and organize themselves in a period-adding bifurcatio...

In this paper we have analyzed the time series obtained from an experimental realization of an inductorless version of Chua’s circuit. We have also compared the experimental results with the results emerging by analysis of the time series obtained by numerical simulations of the respective model equations. Lyapunov exponent spectra, the Kaplan–York...

We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor R as the control parameter and varying from 1300 Ω to 2000 Ω. Experimental time series at fixed R were used to reconstruct attractors by the delay vector technique. The flow attr...

In this work, we have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor R as the control parameter and varying from 1300Ω to 2000Ω. The measurements were carried with a 16bit data acquisition interface. Attractors were reconstructed by t...

We measured resistivity in the range of 30–390 K on four semi-insulating low-temperature grown molecular-beam epitaxy GaAs samples. The growth temperature range was from 215 °C to 315 °C. Arrhenius fittings with T−1 and hopping fitting with T−1/4 do not permit us the definition of the temperature ranges controlled by band and hopping conduction, re...

Semi-insulating GaAs samples show low-frequency current oscillations (LFO) under high dc voltage. These spontaneous oscillations are caused by traveling high-electric-field domains and can be explained based on the well-accepted model of electron trapping in deep levels by multiphonon emission processes. This paper aims to explain today the most im...

We investigated the effect of adding the field-dependent recombination process, namely field-enhanced trapping, to the generation-recombination processes of charge carriers that model current oscillations in semiconductors. The main new features arising from this modification are identified in bifurcation diagrams with the electric field as the con...

We present an experimental study of bifurcation diagrams from low frequency current oscillations (LFO) measurements obtained from semi-insulating GaAs samples grown by low temperature molecular beam Epitaxy (LT-MBE). The considered growth temperatures were 215ºC and 265ºC. LFO are considered to be spontaneously generated oscillations under constant...

Electric transport properties measured by Van der Pauw resistivity experiments of Low-Temperature Molecular Beam Epitaxy (LT-MBE) GaAs samples are used to identify a method to improve the resistivity of GaAs material. We present results on five samples grown at 265, 310, 315, 325, and 345 ºC. The electric measurements were carried out at temperatur...

We have analyzed the nonlinear electric field time series theoretically generated by a set of three coupled first-order differential equations in order to interpret the chaotic behavior present in measurements of low-frequency current oscillations in semiconductor samples. In the present work, we carry out a direct investigation of the theoretical...

Low frequency oscillations (LFO) on current I(V, t) curves were studied in a GaAs sample grown by molecular beam epitaxy. Our measurements were carried out at a temperature of 200 K and under infrared illumination. The nonlinear I(V) characteristics give rise to spontaneous oscillations under constant applied bias V. The attractors were constructed...

We have carried out van der Pauw resistivity and Hall effect measurements on a series of Molecular Beam Epitaxy InAs/GaAs superlattice samples containing InAs quantum dots. Three growth parameters were varied, the InAs coverage, the number of repetitions of the InAs/GaAs layers, and the GaAs spacer thickness. The results can be grouped in two sets,...

Studying the transport properties via Hall and resistivity measurements of low-temperature molecular-beam epitaxy (LT-MBE) GaAs samples, the optimal conditions for fabricating high-resistivity material are found. We present results on three LT-MBE GaAs samples grown at 215, 265, and 315 °C. The measurements were carried out at temperatures ranging...

We have observed low frequency current oscillations in a semi-insulating GaAs sample grown by low temperature molecular beam epitaxy. For this, an experimental setup proper to measure high impedance samples with small external noise was developed. Spontaneous oscillations in the current were observed for some bias conditions. Although measurements...

Semi-insulating GaAs samples present N-shaped negative differential conductivity under high-electric fields. This behavior can be associated with two physical processes: Impact ionization (generation) and field-enhanced trapping (recombination), both of which involve trapped and free electrons. We have analyzed the j(E) characteristic curves of a G...