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1.
A. Yu. Kolesov E. F. Mishchenko N. Kh. Rozov 《Proceedings of the Steklov Institute of Mathematics》2007,259(1):101-127
We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate
from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by
a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit
RCL oscillator with delay in a feedback loop. 相似文献
2.
A. Yu. Kolesov E. F. Mishchenko N. Kh. Rozov 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):206-222
The well-known sine-Gordon equation, supplemented with small damping and small quasiperiodic external force, is studied under the zero Dirichlet boundary conditions at the endpoints of a finite interval. The main assumption is that all frequencies of the external force are in 1:1 resonance with certain eigenfrequencies of the unperturbed equation; i.e., the socalled fundamental multifrequency resonance is observed. It is shown that in this case, by an appropriate choice of the parameters of the external force, one can make it so that the boundary value problem has a stable invariant torus of any finite dimension that bifurcates from zero on any preassigned finite set of spatial modes. It is also shown (by numerical analysis) that in a number of cases the above-mentioned torus coexists with a chaotic attractor. 相似文献
3.
A. I. Artem’ev D. N. Klochkov K. Oganesyan Yu. V. Rostovtsev M. V. Fedorov 《Laser Physics》2007,17(10):1213-1216
The spatial amplification of a wave in a magnetostatic undulator with noncollinear electron and laser beams is studied in the framework of the dispersion relation for single-frequency and collective regimes. The dependence of the gain on the electron beam width is estimated with regard to the spatial boundedness of the beams. The laser power threshold at which the selection with respect to the transverse velocity is possible is obtained for a free-electron laser without inversion. 相似文献
4.
A. Yu. Kolesov E. F. Mishchenko N. Kh. Rozov 《Proceedings of the Steklov Institute of Mathematics》2007,259(2):101-127
We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate
from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by
a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit
RCL oscillator with delay in a feedback loop.
Original Russian Text ? A.Yu. Kolesov, E.F. Mishchenko, N.Kh. Rozov, 2007, published in Trudy Matematicheskogo Instituta imeni
V.A. Steklova, 2007, Vol. 259, pp. 106–133. 相似文献
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We propose a general idea of obtaining different chains of coupled oscillators with chaotic buffering. As examples, we consider chains of diffusively coupled generalized cubic Schrödinger equations and nonlinear telegraph equations. We also give examples of systems that have an infinite-dimensional chaotic attractor. 相似文献
7.
Alexei Yu. Lukin Sergei V. Shevyakov Alexei V. Laptev Olga I. Davydova Vitali I. Shvets Olga V. Demina Yury P. Strokach Valery A. Barachevsky Michail V. Alfimov Sergei P. Gromov Artem I. Vedernikov Johan Lugtenburg Andrey A. Khodonov 《Journal of inclusion phenomena and macrocyclic chemistry》2004,49(1-2):153-161
An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C2- and C5-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed. 相似文献
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