Analysis of the formation of structures and chaotic dynamics in a nonrelativistic electron beam with a virtual cathode in the presence of a decelerating field

A nonrelativistic electron beam with a virtual cathode situated in the diode gap with a decelerating field is experimentally and theoretically studied. A 1D model of the electron beam in the presence of a decelerating field is constructed. Nonlinear nonstationary processes in this system are investigated by means of numerical analysis of the model. The processes are described and interpreted with regard to formation and interaction of structures in the electron flow. The theoretical results are qualitatively confirmed by the experimental data showing that the system under study can be considered as a promising controlled source of chaotic oscillations in the microwave range.     

Duration of the process of complete synchronization of two coupled identical chaotic systems

We consider the time required for complete synchronization of two identical one-way coupled van der Pol-Duffing oscillators occurring in the regime of dynamic chaos. The influence of the initial phase difference between oscillators on the duration of the process of complete synchronization has been studied. At a fixed phase of chaotic oscillations of the self-excited drive oscillator, the period of time (past the coupling onset) during which the complete synchronization regime is established depends on the phase of the self-excited response oscillator.     

Effect of external signal on the output power of an oscillator with electron feedback

The effect of an external single-frequency harmonic signal on the output power of an oscillator with electron feedback has been studied by analytical and numerical methods. It is established that an increase in the input signal power leads to sharp growth in the output power of the nonautonomous oscillator. Physical processes that take place in the electron beam with virtual cathode under the action of an external harmonic signal, which leads to velocity modulation in the electron beam entering the interaction space, have been analyzed. The obtained results well agree with the data of previous experimental investigations of the signal gain in a low-voltage vircator.     

Noise-induced binary synchronization in nonlinear systems

The phenomenon of noise-induced binary synchronization has been discovered in two independent dynamical systems generating aperiodic binary signals under the action of a common noise source. The presence of a synchronous regime was confirmed by the calculation of Lyapunov exponents for the two systems. The mechanism of development of the noise-induced binary synchronization regime has been found. A relation of the observed regime to binary generalized synchronization is established.

     

The influence of the coupling mutuality degree on the onset of various types of chaotic synchronization

The influence of the degree of coupling mutuality on the onset of the regimes of complete, lag, phase, and generalized synchronization is studied. It is shown that the thresholds of onset of synchronous regimes generally decrease with increasing degree of coupling mutuality between oscillators. It is also found that, for the regime of generalized synchronization in the region of relatively large frequency mismatch, the threshold of onset of synchronous regime weakly depends on the coupling mutuality coefficient.     

3D simulation of electron beam squeezed-state generation in a two-section drift tube and analysis of its characteristics

A 3D numerical electromagnetic simulation of a vircator in the mode of electron-beam squeezedstate generation is performed. Detailed numerical investigations are carried out, and the dynamics of charged particles in the squeezed state is analyzed. It is shown that the electron beam density (and, as a consequence, effective beam plasma frequency) can be significantly increased in the squeezed state. Hence, the vircator generation frequency and power can also be increased.     

On the possibility of increasing the automodulation threshold in a gyro-oscillator with backward-wave and coupled electrodynamic systems

We have studied the possibility of increasing the onset threshold for automodulation caused by a growth in the beam current in gyro-backward-wave tubes. It is shown that, by using a coupled electrodynamic system, it is possible to significantly shift the region of threshold currents for the automodulation onset so as to increase the output power in a singe-frequency generation regime.     

Mechanisms complicating the dependence of the transient process duration on the initial conditions in two-dimensional maps

Mechanisms leading to complication of the dependence of a transient process duration on the initial conditions upon a change in control parameters of a two-dimensional dynamical system with discrete time (Eno map) are considered. It is shown that the character of this dependence for a stable cycle is determined by multiplicators. A change in the control parameters in the same dynamical regime produces a bifurcation leading to reclosure of the stable and unstable manifolds. This results in a qualitative complication of the dependence of the transient process duration on the initial conditions in the system.     

A new type of one-dimensional discrete map

A one-dimensional two-parameter map whose behavior on the plane of control parameters qualitatively reproduces the dynamics of a flow system — an rf oscillator describable by a system of three ordinary differential equations. It is it is shown that that the behavior of the map largely coincides with that of the flow system and is also similar to the results of a previous experiment on the rf oscillator. Pis’ma Zh. Tekh. Fiz. 24, 1–8 (September 17, 1998)     

Self-similarity of the desynchronization process in a network of generalized Kuramoto oscillators

The phenomenon of explosive synchronization in a network of generalized Kuramoto oscillators is considered. It has been shown that this process results from self-similarity observed after the loss of stability by synchronous clusters of different dimensions. The appearance of self-similarity can be revealed when studying the processes of destruction in the synchronous state of a network. It has been demonstrated that a system passes through a sequence of self-similar configurations of interacting oscillators after the abrupt destruction of a synchronous regime.