[en] The slow-fast effect in a vector field with a codimension-two double Hopf bifurcation at the origin is investigated in the paper. To explore the typical evolution of the dynamics, the universal unfolding of the normal form of the vector field is taken into consideration. When the parametric excitation is introduced, the frequency of which is far less than the two natural frequencies, slow-fast behaviors may appear. Regarding the whole parametric excitation term as a slow-varying parameter, the equilibrium branches and the bifurcations of the generalized autonomous fast subsystem can be derived. With the variation of the exciting amplitude, different types of bursting oscillations caused by the coupling of two scales in frequency domain may appear, the mechanism of which are obtained by employing the overlap of the transformed phase portraits and the equilibrium branches as well as the bifurcations of the fast subsystem. It is found that, for relatively small exciting amplitude, no bifurcation of the fast subsystem occurs, and the system behaves in quasi-periodic oscillations. With the increase of the exciting amplitude, different types of bifurcations may take place, leading to the single-mode bursting oscillations, which may evolve to mixed-mode bursting oscillations. Symmetric breaking bifurcations result in the transitions between a symmetric attractor and two co-existed asymmetric attractors in the system. Furthermore, for the mixed-mode bursting oscillations, the trajectory may alternate between the single-mode oscillations and the mixed-mode oscillations via bifurcations of the equilibrium branches, causing the synchronization and non-synchronization between different state variables. (paper)

[en] Highlights: • Bursting oscillations of the vector field with a Double Hopf bifurcation are observed. • Bifurcation mechanism of bursting oscillations is presented. • Different forms of bursting oscillations with both single mode and mixed modes are obtained. Up to now, most of the work related to the slow-fast dynamical systems are based on the low dimensional systems with only codimension-one bifurcations at the transitions between the quiescent states and the spiking states, while there usually only exists one slow variable in the system. Since the coupling effect of two scales on the behaviors of high dimensional systems with two or more slow variables as well as high co-dimensional bifurcations lacks exploration, in this paper, we investigate the slow-fast effect on a 6-dimension system, which can be regarded as the coupling of two subsystems. The fast subsystem is expressed as the normal form of the vector field with a double Hopf bifurcation at the origin, while the slow-varying parameter in the fast subsystem is controlled by the slow subsystem. For the fast subsystem, the trajectory is projected onto two independent sub-planes for better observation, and the movement of bursting oscillators can be synthesized with information from each dimension. In the sub-plane, the mechanism of bursting oscillations is derived by employing the overlap of the transformed phase portrait and the equilibrium branches as well as the bifurcations. It is found that, Hopf bifurcation sets may cause the fast subsystem to transform between the single mode and the mixed-mode or between different single modes, leading to bursting oscillations in certain sub-planes or the whole four dimensions of the fast subsystem. Furthermore, interesting phenomena may be caught, such as the trajectory jumping in the process of oscillation as well as transforming between different oscillation modes of the fast subsystem by the way of jump as a result of the fold bifurcation set.

[en] The composite particles composed of quantum dots coated with silica and grafted with copolymer of polyethylene glycol and low molecular weight polyethylene terephthalate (QDs@SiO₂-PEG-LMPET) are synthesized. The internal QDs provide luminescent performance and combine with SiO₂ to form QDs@SiO₂ with good dispersion to solve the defect that small-sized SiO₂ is prone to agglomerate. The block polymer LMPET-PEG grafted on the surface can make the composite particles better compatible with the PET matrix. In summary, QDs@SiO₂-PEG-LMPET not only play the same role as SiO₂ to enhance the crystallization performance of PET matrix, but also provide stable luminescence performance, which is multifunctional additive with broad application prospects. (paper)

[en] A nonenzymatic electrochemical glucose sensor is described that was obtained by in situ photodeposition of high-density and uniformly distributed palladium nanoparticles (PdNPs) on a porous gallium nitride (PGaN) electrode. Cyclic voltammetric and chronoamperometric techniques were used to characterize the performance of the modified electrode toward glucose. In 0.1 M NaOH solution, it has two linear detection ranges, one from 1 μM to 1 mM, and another from 1 to 10 mM, and the detection limit is 1 μM. The electrode is repeatable, highly sensitive, fast and long-term stable. It was applied to the quantitation of serum glucose where it displayed accurate current responses.

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[en] Highlights: • The Cu₂O/CNTs composite electrocatalysts are fabricated by green electroless plating. • Using glucose instead of formaldehyde as reducing agent for electroless plating. • The electroless plating does not require purification, sensitization, and activation. • Cu₂O/CNTs exhibits high HER activity with overpotential of 101 mV at −10 mA/cm^2. • Cu₂O/CNTs reveals good operational stability after 20 h continuous test at −0.1 V. Cuprous oxide (Cu₂O) nanoparticles supported on pristine carbon nanotubes (Cu₂O/CNTs) were synthesized by a facile and green electroless plating method, in which glucose replaced formaldehyde as the reducing agent. The as-prepared Cu₂O/CNTs nanocomposite materials as electrocatalysts exhibited remarkable electrocatalytic activity towards hydrogen evolution reaction in alkaline solution, with an overpotential of 101 mV at −10 mA cm⁻² and a Tafel slope of 88 mV dec⁻¹. In addition, Cu₂O/CNTs electrocatalysts maintained high electrocatalytic activity after the accelerated durability tests in 0.1 M KOH. All these results indicated Cu₂O/CNTs can be utilized as efficient HER electrocatalysts for water splitting.