Modulation instability of an electromagnetic wave interacting with a counterpropagating electron beam under condition of cyclotron resonance absorption.

In this paper, transmission of a monochromatic wave through a counterpropagating electron beam under the condition of cyclotron resonance absorption is studied by theoretical analysis and numerical simulation. Conditions of the modulation instability (MI) are analyzed. The MI strongly affects the regimes of transmission.

Entrainment, stopping, and transmission of microwave solitons of self-induced transparency in counter-propagating magnetized electron beam.

Based on numerical simulations of a boundary problem, we study various scenarios of microwave soliton formation in the process of cyclotron resonance interaction of a short electromagnetic pulse with a counter-propagating initially rectilinear electron beam taking into account the relativistic dependence of the cyclotron frequency on the electrons' energy. When a certain threshold in the pulse energy is exceeded, the incident pulse can propagate without damping in the absorbing beam, similar to the effect of self-induced transparency in optics. However, mutual motion of the wave and electrons can lead to some novel effects.

Bifurcation analysis of multistability of synchronous states in the system of two delay-coupled oscillators.

Systems of mutually coupled oscillators with delay coupling are of great interest for various applications in electronics, laser physics, biophysics, etc. Time delay usually originates from the finite speed of propagation of the coupling signal. In this paper, we present the results of detailed bifurcation analysis of two delay-coupled limit-cycle (Landau-Stuart) oscillators.

Phase locking of two limit cycle oscillators with delay coupling.

Mutual phase locking in the system of two limit cycle oscillators with delay coupling is studied. Conditions of phase locking are derived as a result of analysis of a generalized Adler equation. The analytical results are compared with numerical simulation.

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator.

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities.