We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic functions as a special case. Also, for bounded planar harmonic mappings, we obtain results similar to a theorem of Landau on bounded holomorphic functions.
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 differential 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.
Multi-channel soft x-ray (SX) detectors are applied to generate images of
magnetohydrodynamic (MHD) oscillation on the HT-7 tokamak, and the data
from SX cameras are analysed by using the
Fourier--Bessel harmonic reconstruction method and the singular value
decomposition. The image
reconstruction of SX emissivity is obtained on the assumption of plasma
rigid rotation. One of the important phenomena in the HT-7 discharge is the
transition from the sawtooth oscillations to the MHD oscillations when the
plasma density grows higher. The MHD structure
observed in the SX tomography is featured as follows: the magnetic surface of MHD
structure is made up of the crescent-shaped ``hot core' and the circular
``cold bubble'. The structure of the magnetic surface is relatively stable.
It rotates in the direction of the electron diamagnetic drift at a
frequency being the oscillation frequency of the MHD oscillations. 相似文献
In this paper, the fractional-order Genesio--Tesi system showing chaotic
behaviours is introduced, and the corresponding one in an integer-order form
is studied intensively. Based on the harmonic balance principle, which is
widely used in the frequency analysis of nonlinear control systems, a
theoretical approach is used to investigate the conditions of system
parameters under which this fractional-order system can give rise to a
chaotic attractor. Finally, the numerical simulation is used to verify the
validity of the theoretical results. 相似文献
We report a detailed theoretical study of current oscillation and dc-voltage-controlled chaotic dynamics in doped GaAs/AlAs resonant tunneling
superlattices under crossed electric and magnetic fields. When the
superlattice is biased at the negative differential velocity region, current
self-oscillation is observed with proper doping concentration. The current
oscillation mode and oscillation frequency can be affected by the dc voltage bias, doping density, and magnetic field. When an ac electric field with fixed amplitude and frequency is also applied to the system, different nonlinear properties show up in the external circuit with the change of dc voltage bias. We carefully study these nonlinear properties with different
chaos-detecting methods. 相似文献