Dynamic analysis of fractional-order neural networks with inertia

The existence and the S-asymptotic ω-periodic of the solution in fractional-order Cohen-Grossberg neural networks with inertia are studied in this paper. Based on the properties of the Riemann-Liouville (R-L) fractional-order derivative and integral, the contraction mapping principle, and the Arzela-Ascoli theorem, sufficient conditions for the existence and the S-asymptotic ω-period of the system are achieved. In addition, an example is simulated to testify the theorem

<i>N</i>‑Annulated Perylene as An Efficient Electron Donor for Porphyrin-Based Dyes: Enhanced Light-Harvesting Ability and High-Efficiency Co(II/III)-Based Dye-Sensitized Solar Cells

Porphyrin-based dyes recently have become good candidates for dye-sensitized solar cells (DSCs). However, the bottleneck is how to further improve their light-harvesting ability. In this work, <i>N</i>-annulated perylene (NP) was used to functionalize the Zn-porphyrin, and four “push–pull”-type NP-substituted and fused porphyrin dyes with intense absorption in the visible and even in the near-infrared (NIR) region were synthesized. Co­(II/III)-based DSC device characterizations revealed that dyes <b>WW-5</b> and <b>WW-6</b>, in which an ethynylene spacer is incorporated between the NP and porphyrin core, showed pantochromatic photon-to-current conversion efficiency action spectra in the visible and NIR region, with a further red-shift of about 90 and 60 nm, respectively, compared to the benchmark molecule <b>YD2-</b><i><b>o</b></i><b>-C8</b>. As a result, the short-circuit current density was largely increased, and the devices displayed power conversion efficiencies as high as 10.3% and 10.5%, respectively, which is comparable to that of the <b>YD2-</b><i><b>o</b></i><b>-C8</b> cell (η = 10.5%) under the same conditions. On the other hand, the dye <b>WW-3</b> in which the NP unit is directly attached to the porphyrin core showed a moderate power conversion efficiency (η = 5.6%) due to the inefficient π-conjugation, and the NP-fused dye <b>WW-4</b> exhibited even poorer performance due to its low-lying LUMO energy level and nondisjointed HOMO/LUMO profile. Our detailed physical measurements (optical and electrochemical), density functional theory calculations, and photovoltaic characterizations disclosed that the energy level alignment, the molecular orbital profile, and dye aggregation all played very important roles on the interface electron transfer and charge recombination kinetics

N -annulated perylene as an efficient electron donor for porphyrin-based dyes: Enhanced light-harvesting ability and high-efficiency Co(II/III)-based dye-sensitized solar cells

10.1021/ja409291gJournal of the American Chemical Society1361265-272JACS