Desynchronization of Large Scale Delayed Neural Networks

We consider a ring of identical neurons with delayed nearest neighborhood inhibitory interaction. Under general conditions, such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay di erential equation with negative feedback. Despite the fact that the slowly oscillatory periodic solution of the scalar equation is stable, we show that the associated synchronous solution is unstable if the size of the network is large

Analysis and Design of Nanoantennas

Ph.DDOCTOR OF PHILOSOPH

Influences of Random Surface Waves on the Estimates of Wind Energy Input to the Ekman Layer in the Antarctic Circumpolar Current Region

Sea surface waves significantly affect the wind energy input to the Ekman layer in the upper ocean. In the study, we first incorporated the wave-induced Coriolis-Stokes forcing, the reduction of wind stress caused by wave generation, and wave dissipation into the classical Ekman model to investigate the kinetic energy balance in the wave-affected Ekman layer. Then, both the theoretical steady state solution for the idealized condition and the nonsteady state solution for the realistic ocean were derived. Total energy input to the wave-affected Ekman layer includes the wind stress energy input and the wave-induced energy input. Based on the WAVEWATCH III model, the wave spectrum was simulated to represent realistic random directional wave conditions. The wind stress energy input and the wave-induced energy input to the wave-affected Ekman layer in the Antarctic Circumpolar Current in the period from 1988 to 2010 were then calculated. The annual mean total energy input in the Antarctic Circumpolar Current region was 402.5 GW and the proportions of the wind stress energy input and the wave-induced energy input were, respectively, 85% and 15%. Particularly, total energy input in the Antarctic Circumpolar Current in the wave-affected Ekman layer model was 59.8% lower than that in the classical Ekman model. We conclude that surface waves play a significant role in the wind energy input to the Ekman layer