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.

Novel optical PVC probes for on-site detection/determination of fluoroquinolones in a solid/liquid interface: Application to the determination of Norfloxacin in aquaculture water

A novel optical disposable probe for screening fluoroquinolones in fish farming waters is presented, having Norfloxacin (NFX) as target compound. The colorimetric reaction takes place in the solid/liquid interface consisting of a plasticized PVC layer carrying the colorimetric reagent and the sample solution. NFX solutions dropped on top of this solid-sensory surface provided a colour change from light yellow to dark orange. Several metals were tested as colorimetric reagents and Fe(III) was selected. The main parameters affecting the obtained colour were assessed and optimised in both liquid and solid phases. The corresponding studies were conducted by visible spectrophotometry and digital image acquisition. The three coordinates of the HSL model system of the collected image (Hue, Saturation and Lightness) were obtained by simple image management (enabled in any computer). The analytical response of the optimised solid-state optical probe against concentration was tested for several mathematical transformations of the colour coordinates. Linear behaviour was observed for logarithm NFX concentration against Hue+Lightness. Under this condition, the sensor exhibited a limit of detection below 50 μM (corresponding to about 16 mg/mL). Visual inspection also enabled semi-quantitative information. The selectivity was ensured against drugs from other chemical groups than fluoroquinolones. Finally, similar procedure was used to prepare an array of sensors for NFX, consisting on different metal species. Cu(II), Mn(II) and aluminon were selected for this purpose. The sensor array was used to detect NFX in aquaculture water, without any prior sample manipulation.