Applied Problems of Nonlinear Oscillation and Wave Theory

Dynamics of two phase-locked-loop systems with low-inertia control loops coupled through the phase discriminator is investigated. Stability of synchronous modes of the ensemble is considered. Mechanisms of arising of quasi-synhronous oscillations are studied. Domains of existence of synchronous and quasi-synhronous modes are analysed.

A two-dimensional model exhibiting the chaotic spiking-bursting activity of real neurons is proposed. The model is given by the discontinuous two-dimensional map. It is constructed on the basis of the discrete modification of the FitzHugh–Nagumo model and one-dimensional Lorenz type map. We have studied the dynamics of the system, found the conditions on the parameters under which chaotic attractor exists. The structure and properties of the attractor is studied. This attractor mimics spiking-bursting oscillations.

We suggest the model of ensemble of resource sharing oscillators in the form of one-dimension array of self-sustained systems with N-type nonlinearity. We analyze the mechanism of oscillatory cluster formation, study the intra-cluster synchronization, and show the effect of energy fluctuations.

Исследованы характерные колебательные режимы и нелинейные эффекты, возникающие в условиях особого типа связи, который широко распространен в природе. А именно, во многих случаях взаимодействие в ансамбле осцилляторов осуществляется посредством потребления и распределения некоего энергонесущего ресурса. Динамика таких систем имеет ряд особенностей. В первой части работы показано, как детализация модели авторегуляции почечного кровотока приводит к системе интересующего нас класса и каковы ее типичные динамические режимы.

The complex oscillatory movements of eyes at nistagm are investigated. The results of analysis of difficult fluctuating motions of eyes at nistagm and character of changes at periodic light influence are resulted. The type of nistagm for patients, at which present simultaneously both horizontal and vertical motions, it’s described.

The nonlinear system of non-markovian type kinetic equations, describing the particles production with varying masses in framework of Nambu–Jona-Lasinio model is investigated for the case of p-meson production by s-meson decay in hot and dense nuclear matter. The p-meson enhancement in a low-momentum region due to additional s-mesons creation via intertial mechanism using the nonlinear dependence of sigmas mass from the temperature in equation of state in vicinity of ms ¼ 2mp is calculated.

In the paper, the noval hybrid microwave electronic device based on a traveling wave tube and multisectional collector with virtual cathode is suggested and experimentally investigated. The virtual cathode is formed in the electron beam by applying a braking electric field in the collector, i.e. in the part of the device following to the interaction space of traveling wave tube. It is shown, that microwave broad band chaotic signals are generated and amplified in the device. The corresponding curve has the negligible cutting.

We examine regimes of magnetron corresponding to the temperature limitation conditions and spatial charge emission limitation. We discover the greater chaos of trajectories and their long presence near cathode to be in the later case; as calculations show this phenomenon may cause the abnormal noise to appear in devices of magnetron type with a central cathode.

The numerical scheme for calculation the set of Lyapunov exponents in distributed systems with delayed feedback based on a modification of Benettine algorithm is described. The results of numerical simulation of two such systems (active oscillator with cubic nonlinearity and active oscillator of klystron type) are presented. The sets of Lyapunov exponents in different regimes, particularly in regimes of «weak» and «developed» chaos are analyzed. The calculation peculiarities of the set of Lyapunov exponents in the systems with delayed feedback are discussed.

On purpose to explain the wire swinging phenomenon in electro-transmission lines the investigation of the self-oscillations in a real-like model of a thermo-mechanical systemis performed.