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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.

The possibility of heavy ion additional acceleration in laser beams is investigated. The main observation is the existence of a big variety of acceleration modes due to many fitting parameters even for only one Gaussian beam and for crossed ones even more so. An essentially non-monotonic dependence of energy gain on relevant variables such as initial velocity or pulse duration is found which makes the search for the most effective acceleration modus very complex. There is a threshold level for the intensity (» 1025W/cm2) when the ion moves in the capture mode in one direction.

Population dynamics of highly excited states of a hydrogen atom under the action of an ultra-short intense laser pulse is studied by means of direct numerical solution of  Schr¨ edinger equation in the finite basis of eigenstates of the discrete and continuous energy spectrum. The essential role of continuous spectrum states is demonstrated. Formation of localized wave packets of Rydberg states is discussed.

The dynamics of populations of 4s and 3p states in hydrogen atom is investigated under the action of ultra high laser single frequency linear-polarized pulse at one-, two- and three-photon resonance and at large detuning out of frame of perturbation theory and rotating wave approximation. It was shown the existence of low frequency modulation of optical oscillations,which frequency becomes zero at some values of laser field amplitude.

Fully vectorial plane wave method is presented aimed the calculation of the electromagnetic eigenwaves in periodical dielectric media having arbitrary geometry and dimension with both isotropic and anisotropic elements. Using this method the effect of the reorientation of molecules of anisotropic material in photonic crystal on the dispersion surface is investigated.

The results of numerical modelling of the supercontinuum generation in microstructure fibers excited by femtosecond multi-soliton pulses are presented. Pulse dynamics is modelled using the extended Schrodinger equation, in which the dispersion and nonlinear coefficient for given fiber are calculated by plane wave method. It is more easy to achieve the phase-matching conditions for the dispersive wave generation in the fibers with periodical modulated diameter.

Problems for students are presented to be solved with computer for the educational course «Dynamical Chaos». The set of problems covers topics from the nature of chaos to the scenarios of its appearance. Methodical recommendations are given.

Problems for students are presented to be solved with computer for the educational course «Dynamical Chaos». The set of problems covers topics from the nature of chaos to the scenarios of its appearance. Methodical recommendations are given.

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.

Changes in the dynamics of renal blood flow at the transition from the microscopic level of individual nephrons to the macroscopic level of the whole kidney are investigated. Rhythmic processes caused by the auto-regulatory mechanisms and their interactions in the form of synchronization and modulation are analyzed. Distinctions of the dynamics in the cases of normal and increased arterial pressure are discussed.