Applied Problems of Nonlinear Oscillation and Wave Theory

The influence of a pulse train on the dynamics of unidirectly nonlinearly coupled Hindmarsh-Rose neurons is investigated. The synchronization of the spike-generating neuron by the periodical pulse train is studied. Information and dynamical aspects of burst generation under the action of a pulse train with irregular interpulse intervals are analyzed. It is shown that the backward burst-to-spike transformation by the neuron at rest is possible. Dynamic unreliability during the spike-to-burst transformation is explained qualitatively.

Emission characteristics of autoemitters with a various relief of a Surface are investigated. It is experimentally shown, that reduction of a backlash in microdiod devices inevitably leads to significant growth of macroscopical intensity of an electrostatic field at the set size of an autoemission current.

The possibility of reconstruction of complex unharmonic motion function of subject was investigated using autodyne interference system. Experimental results of parameter determination of complex unharmonic motion of reflector were presented. It was shown that application of manystages digital filtration of autodyne experimental signal allows to decrease influence of noise distortion on reconstruction signal.

Based on the parabolic differential equation solution behaviour of the pulse width at half-height in linear second order dispersion media was analyzed. It was shown that rectangular non-chirped pulse width varies non-monotonously with distance and reaches 50–60% initial width at compression length that is equal to 0.44 dispersive length. This compression was shown to be caused by dispersive pulse-edges perturbations that lead to frequency chirp on pulse top.

We study the formation of multiple synchronous states for weakly diffusively coupled 3D-oscillators. As a representative 3D-model we use the equations for generator with inertial nonlinearity. It is shown that oscillations multi-crest waveform is not the factor that solely defines the number of multiple synchronous states, but dephasing-like effects have to be taken into account.

We study the formation of multiple synchronous states for weakly diffusively coupled 3D-oscillators. As a representative 3D-model we use the equations for generator with inertial nonlinearity. It is shown that oscillations multi-crest waveform is not the factor that solely defines the number of multiple synchronous states, but dephasing-like effects have to be taken into account.

The work proposed a modification of support vector machines (SVM) to train and classify in real time (online) streams of data. The algorithm is tested on the data handwriting figures and shown that its error is comparable to SVM direct solution error. Speed and support vectors number of proposed SVM algorithm is smaller than in other known SVM implementations. Finally, a ternary classificator for 2-class problem is proposed which shows better results than binary.

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We consider dynamics in a pair of nonlinearly coupled pendulums. With existence of dissipation and constant torque such system can demonstrate in-phase periodical rotation in addition to the stable state. We have shown in numerical simulations that such in-

The hydrodynamic equations of inviscid compressible fluid are converted to a form suitable for development of self-consistent theory of interaction of hydrodynamic flows with resonators and periodic structures by analogy with the theory of microwave electronics devices with crossed electric and magnetic fields. We consider excitation of the acoustic velocity fields by the sources provided by vorticity in the flow.

This article contains the information concerning the organization of the All-Russian scientific school in the Saratov State University for young scientists. The paper deals with the reviews of the lectures, labs, practical tasks, etc. The scientists from different regions of Russia have taken part in this school.