15 research outputs found
Generalized Synchronization in Ginzburg-Landau Equations with Local Coupling
The establishment of generalized chaotic synchronization in Ginzburg-Landau
equations unidirectionally coupled at discrete points of space (local coupling)
has been studied. It is shown that generalized syn-chronization regimes are
also established with this type of coupling, but the necessary intensity of
coupling issignificantly higher than that in the case of a spatially
homogeneous couplingComment: 4 pages, 2 figure
Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations
Generalized synchronization is analyzed in unidirectionally coupled
oscillatory systems exhibiting spatiotemporal chaotic behavior described by
Ginzburg-Landau equations. Several types of coupling betweenthe systems are
analyzed. The largest spatial Lyapunov exponent is proposed as a new
characteristic of the state of a distributed system, and its calculation is
described for a distributed oscillatory system. Partial generalized
synchronization is introduced as a new type of chaotic synchronization in
spatially nonuniform distributed systems. The physical mechanisms responsible
for the onset of generalized chaotic synchronization in spatially distributed
oscillatory systems are elucidated. It is shown that the onset of generalized
chaotic synchronization is described by a modified Ginzburg-Landau equation
with additional dissipation irrespective of the type of coupling. The effect of
noise on the onset of a generalized synchronization regime in coupled
distributed systems is analyzed.Comment: 12 page
Experimental and Theoretical Investigation into the Effect of the Electron Velocity Distribution on Chaotic Oscillations in an Electron Beam under Virtual Cathode Formation Conditions
The effect of the electron transverse and longitudinal velocity spread at the
entrance to the interaction space on wide-band chaotic oscillations in intense
multiple-velocity beams is studied theoretically and numerically under the
conditions of formation of a virtual cathode. It is found that an increase in
the electron velocity spread causes chaotization of virtual cathode
oscillations. An insight into physical processes taking place in a virtual
cathode multiple velocity beam is gained by numerical simulation. The
chaotization of the oscillations is shown to be associated with additional
electron structures, which were separated out by constructing charged particle
distribution functions.Comment: 9 pages, 8 figure
Investigation of the Chaotic Dynamics of an Electron Beam with a Virtual Cathode in an External Magnetic Field
The effect of the strength of the focusing magnetic field on chaotic dynamic
processes occurring inan electron beam with a virtual cathode, as well as on
the processes whereby the structures form in the beamand interact with each
other, is studied by means of two-dimensional numerical simulations based on
solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as
the focusing magnetic field is decreased,the dynamics of an electron beam with
a virtual cathode becomes more complicated due to the formation andinteraction
of spatio-temporal longitudinal and transverse structures in the interaction
region of a vircator. The optimum efficiency of the interaction of an electron
beam with the electromagnetic field of the vircator isachieved at a
comparatively weak external magnetic field and is determined by the
fundamentally two-dimensional nature of the motion of the beam electrons near
the virtual cathode.Comment: 12 pages, 8 figure
Mechanisms Behind the Generalized Synchronization Conditions
A universal mechanism underlying generalized synchronization conditions in
unidirectionally coupled stochastic oscillators is considered. The
consideration is carried out in the framework of a modified system with
additional dissipation. The approach developed is illustrated with model
examples. The conclusion is reached that two types of the behavior of nonlinear
dynamic systems known as generalized synchronization and noise-induced
synchronization, which are viewed as different phenomena, actually represent a
unique type of the synchronous behavior of stochastic oscillators and are
caused by the same mechanism.Comment: 8 pages, 5 figure