Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Um novo gerador central de padrões de locomoção para geração de trajectórias em tempo real de robôs quadrúpedes

Neste trabalho estuda-se a geração de trajectórias em tempo real de um robô quadrúpede. As trajectórias podem dividir-se em duas componentes: rítmica e discreta. A componente rítmica das trajectórias é modelada por uma rede de oito osciladores acoplados, com simetria 4 2 Z  Z . Cada oscilador é modelado matematicamente por um sistema de Equações Diferenciais Ordinárias. A referida rede foi proposta por Golubitsky, Stewart, Buono e Collins (1999, 2000), para gerar os passos locomotores de animais quadrúpedes. O trabalho constitui a primeira aplicação desta rede à geração de trajectórias de robôs quadrúpedes. A derivação deste modelo baseia-se na biologia, onde se crê que Geradores Centrais de Padrões de locomoção (CPGs), constituídos por redes neuronais, geram os ritmos associados aos passos locomotores dos animais. O modelo proposto gera soluções periódicas identificadas com os padrões locomotores quadrúpedes, como o andar, o saltar, o galopar, entre outros. A componente discreta das trajectórias dos robôs usa-se para ajustar a parte rítmica das trajectórias. Este tipo de abordagem é útil no controlo da locomoção em terrenos irregulares, em locomoção guiada (por exemplo, mover as pernas enquanto desempenha tarefas discretas para colocar as pernas em localizações específicas) e em percussão. Simulou-se numericamente o modelo de CPG usando o oscilador de Hopf para modelar a parte rítmica do movimento e um modelo inspirado no modelo VITE para modelar a parte discreta do movimento. Variou-se o parâmetro g e mediram-se a amplitude e a frequência das soluções periódicas identificadas com o passo locomotor quadrúpede Trot, para variação deste parâmetro. A parte discreta foi inserida na parte rítmica de duas formas distintas: (a) como um offset, (b) somada às equações que geram a parte rítmica. Os resultados obtidos para o caso (a), revelam que a amplitude e a frequência se mantêm constantes em função de g. Os resultados obtidos para o caso (b) revelam que a amplitude e a frequência aumentam até um determinado valor de g e depois diminuem à medida que o g aumenta, numa curva quase sinusoidal. A variação da amplitude das soluções periódicas traduz-se numa variação directamente proporcional na extensão do movimento do robô. A velocidade da locomoção do robô varia com a frequência das soluções periódicas, que são identificadas com passos locomotores quadrúpedes.

Determination of ametryn in soils via microwave-assisted solvent extraction coupled to anodic stripping voltammetry with a gold ultramicroelectrode

An extraction-anodic adsorptive stripping voltammetric procedure using microwave-assisted solvent extraction and a gold ultramicroelectrode was developed for determining the pesticide ametryn in soil samples. The method is based on the use of acetonitrile as extraction solvent and on controlled adsorptive accumulation of the herbicide at the potential of 0.50 V (vs. Ag/AgCl) in the presence of Britton-Robinson buffer (pH 3.3). Soil sample extracts were analysed directly after drying and redissolution with the supporting electrolyte but without other pre-treatment. The limit of detection obtained for a 10 s collection time was 0.021 µg g-1. Recovery experiments for the global procedure, at the 0.500 µg g-1 level, gave satisfactory mean and standard deviation results which were comparable to those obtained by HPLC with UV detection.

Optimization of QuEChERS procedure coupled to GC-ECD for organochlorine pesticide determination in carrot samples

An optimised version of the Quick, Easy, Cheap, Effective, Rugged and Safe (QuEChERS) method for simultaneous determination of 14 organochlorine pesticides in carrots was developed using gas chromatography coupled with electron-capture detector (GC-ECD) and confirmation by gas chromatography tandem mass spectrometry (GC-MS/MS). A citrate-buffered version of QuEChERS was applied for the extraction of the organochlorine pesticides, and for the extract clean-up, primary secondary amine, octadecyl-bonded silica (C18), magnesium sulphate (MgSO4) and graphitized carbon black were used as sorbents. The GC-ECD determination of the target compounds was achieved in less than 20 min. The limits of detection were below the EUmaximum residue limits (MRLs) for carrots, 10–50 μg kg−1, while the limit of quantification did exceed 10 μg kg−1 for hexachlorobenzene (HCB). The introduction of a sonication step was shown to improve the recoveries. The overall average recoveries in carrots, at the four tested levels (60, 80, 100 and 140 μg kg−1), ranged from 66 to 111% with relative standard deviations in the range of 2– 15 % (n03) for all analytes, with the exception of HCB. The method has been applied to the analysis of 21 carrot samples from different Portuguese regions, and β-HCH was the pesticide most frequently found, with concentrations oscillating between less than the limit of quantification to 14.6 μg kg−1. Only one sample had a pesticide residue (β-HCH) above the MRL, 14.6 μg kg−1. This methodology combines the advantages of both QuEChERS and GC-ECD, producing a very rapid, sensitive and reliable procedure which can be applied in routine analytical laboratories.

Determination of ochratoxin A in bread: evaluation of microwave-assisted extraction using an orthogonal composite design coupled with response surface methodology

An analytical method using microwave-assisted extraction (MAE) and liquid chromatography (LC) with fluorescence detection (FD) for the determination of ochratoxin A (OTA) in bread samples is described. A 24 orthogonal composite design coupled with response surface methodology was used to study the influence of MAE parameters (extraction time, temperature, solvent volume, and stirring speed) in order to maximize OTA recovery. The optimized MAE conditions were the following: 25 mL of acetonitrile, 10 min of extraction, at 80 °C, and maximum stirring speed. Validation of the overall methodology was performed by spiking assays at five levels (0.1–3.00 ng/g). The quantification limit was 0.005 ng/g. The established method was then applied to 64 bread samples (wheat, maize, and wheat/maize bread) collected in Oporto region (Northern Portugal). OTAwas detected in 84 % of the samples with a maximum value of 2.87 ng/g below the European maximum limit established for OTA in cereal products of 3 ng/g.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?