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.

Electroanalytical determination of oxadiazon and characterization of its base-catalyzed ring-opening products

The electrochemical behavior of the hydrolysis products of oxadiazon was studied by cyclic and square-wave voltammetry using a glassy carbon electrode. Maximum currents were obtained at pH 12.8 in an aqueous electrolyte solution containing 30% ethanol and the current did not decrease with time showing that there was little adsorption of the reaction products on the electrode surface. The hydrolysis products of oxadiazon were identi®ed, after isolation and puri®cation, as 1-trimethylacetyl-2-(2,4-dichloro-5-isopropoxyphenyl)-2-ethoxycarbonylhydrazine (Oxa1) and 1-trimethylacetyl-2-(2,4-dichloro-5-isopropoxyphenyl) hydrazine (Oxa2) with redox potentials 0.6Vand 70.1V (vs. Ag=AgCl), respectively. Based on the electrochemical behavior of 1-trimethylacetyl-2-(2,4-dichloro-5-isopropoxyphenyl) hydrazine (Oxa2) a simple electroanalytical procedure was developed for the determination of oxadiazon in commercial products used in the treatment of rice crops in Portugal that contain oxadiazon as the active ingredient. The detection limit was 161074 M, the mean content and relative standard deviation obtained for seven samples of two different commercial products by the electrochemical method were 28.4 0.8% (Ronstar) and 1.9 0.2% (Ronstar GR), and the recoveries were 100.3 5.4% and 101.1 5.3 %, respectively.

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?