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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.

We present the electronic scheme of autonomous generator of two-frequency quasiperiodic motions and the experimental research results of effect of quasi-periodic motions synchronization under the external two-frequency force.

A method is proposed for reconstructing time-delay systems in periodic regime of oscillations. The method is based on the analysis of these systems response to a weak periodic pulse driving. It is shown that proposed method with using of weak driving allows one to recover the delay time of a ring self-oscillating system with time-delayed feedback and to define the order of a model delay-differential equation.

Chaotic dynamics in the systems of coupling nonautonomous van der Pol oscillators with resonance and nonresonance communicator of the signal is considered. For the both models phase map for the period of the external force are show hyperbolic attractor of the Smale–Williams type. In these models features of chaotic dynamics investigated depending on type of the communicator of the signal.

We study the stability of the symmetric and antisymmetric discrete breathers in the monoatomic chain described by potential energy which is a uniform function of the fourth order. It is shown that the change of the stability properties of these two dynamical objects (known as Sievers-Takeno and Page modes, respectively) takes place at the same strength of the inter-site interactions with respect to the on-site interactions. We also present a new method (the «pair synchronization» method) for the discrete breather construction in the arbitrary nonlinear Hamiltonian lattices.

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.