ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


nonlinear dynamics

Trubetskov Scientific School

The School of Corresponding Member of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences, Professor Dmitry Ivanovich Trubetskov is a unique phenomenon widely known to the scientific community both in Russia and abroad. Its includes science, education and a lot of educational activities. The uniqueness of the School of D. I. Trubetskov is that it covers a wide range of current scientific areas: vacuum electronics, magnetoelectronics, nonlinear dynamics, etc. The School of D. I.

Equations with the Fermi–Pasta–Ulam and dislocations nonlinearity

Issue. The class of Fermi–Pasta–Ulam equations and equations describing dislocations are investigated. Being a bright representative of integrable equations, they are of interest both in theoretical constructions and in applied research. Investigation methods. In the present work, a model combining these two equations is considered, and local dynamic properties of solutions are investigated. An important feature of the model is the fact that the infinite set of characteristic numbers of the equation linearized at zero consists of purely imaginary values.

Dynamics of weakly dissipative self-oscillatory system at external pulse influence, which amplitude is depending polynomially on the dynamic variable

Topic and aim. In this work, we study the dynamics of the kicked van der Pol oscillator with the amplitude of kicks depending nonlinearly on the dynamic variable. We choose the expansions of the function cos x in a Taylor series near zero, as functions describing this dependence.

Bifurcations and transitions to chaos in superlattice coupled to external resonator

In this letter we study nonlinear dynamics and transition to chaos in semiconductor superlattice coupled to external linear resonator. We have shown that such system demonstrates chaotic dynamics in wide range of supply voltage, whereas in autonomous superlattice only periodical dynamics exists. Revealed that transition to chaos in system goes through intermittency

Investigation of stability of nonlinear normal modes in electrical lattices

The problems of existence and stability of the symmetry-induced nonlinear normal modes in the electric chain of non-linear capacitors, connected to each other with linear inductors (the model described in Physica D238 (2009) 1228) are investigated. For all modes of this type, the upper limit of the stability region (in amplitude of voltage oscillations on capacitors) as a function of the chain cell number were found. Asymptotic formulas were determined at cell number tends to infinity.

Nonlinear dynamics of synthetic gene regulatory circuits

Built in a cell synthetic gene regulatory elements may function rather independently on the original natural system. Experimental and theoretical studies of small synthetic networks allow for a better understanding of fundamental dynamical mechanisms of gene regulation. This paper gives an introduction to the modern mathematical approaches and methods in this field, primarily in the framework of nonlinear dynamics.

Nonlinear dynamics and acoustic signals generated by periodic impacts of corundum probe on the solid surface

Experimental and theoretical study of nonlinear dynamics and acoustic signals generated by periodic impacts of corundum probe on the solid surface are conducted. In the work two models are considered for the description of experiments: the analytical model based on the laws of conservation of energy and momentum; the model based on the numerical solution of the nonlinear equation of probe motion. It is shown that the acoustic signal amplitude increases in direct proportion to the oscillations probe amplitude.

Models of volume free electron lasers

Several mathematical models of volume free electron lasers are described with the aim of investigation of their nonlinear dynamics. This review includes models of beams of charged particles moving through spatially-periodic systems (photonic crystals). In simulation of volume free electron lasers on the base of photonic crystals made from metallic threads or foils working in the microwave range it was shown the necessity of taking into account dispersion of electromagnetic waves on resonator threads. 

Three-­dimensional simulation of virtode with toroidal cavities

The results of preliminary 3D fully electromagnetic simulation of microwave generator with virtual cathode and external feedback loop (virtode) are discussed in this paper. The feedback is realized by the velocity modulation of electron beam in the accelerating gap of electron gun with the electromagnetic signal taken with output cavity placed in the virtual cathode area.

From theory of oscillations to nonlinear dynamics

The paper deals with the retrospective consideration of course lectures on theory of oscillations in Nizhny Novgorod university and its evolution during more then 70 years.

Pages