Anna V. Kuptsova

Predictable nonwandering localization of covariant Lyapunov vectors and cluster synchronization in scale-free networks of chaotic maps.

Covariant Lyapunov vectors for scale-free networks of Hénon maps are highly localized. We revealed two mechanisms of the localization related to full and phase cluster synchronization of network nodes. In both cases the localization nodes remain unaltered in the course of the dynamics, i.e., the localization is nonwandering. Moreover, this is predictable: The localization nodes are found to have specific dynamical and topological properties and they can be found without computing of the covariant vectors. This is an example of explicit relations between the system topology, its phase-space dynamics, and the associated tangent-space dynamics of covariant Lyapunov vectors.

Radial and circular synchronization clusters in extended starlike network of van der Pol oscillators

Abstract We consider extended starlike networks where the hub node is coupled with several chains of nodes representing star rays. Assuming that nodes of the network are occupied by nonidentical self-oscillators we study various forms of their cluster synchronization. Radial cluster emerges when the nodes are synchronized along a ray, while circular cluster is formed by nodes without immediate connections but located on identical distances to the hub. By its nature the circular synchronization is a new manifestation of so called remote synchronization [33]. We report its long-range form when the synchronized nodes interact through at least three intermediate nodes. Forms of long-range remote synchronization are elements of scenario of transition to the total synchronization of the network. We observe that the far ends of rays synchronize first. Then more circular clusters appear involving closer to hub nodes. Subsequently the clusters merge and, finally, all network become synchronous. Behavior of the extended starlike networks is found to be strongly determined by the ray length, while varying the number of rays basically affects fine details of a dynamical picture. Symmetry of the star also extensively influences the dynamics. In an asymmetric star circular cluster mainly vanish in favor of radial ones, however, long-range remote synchronization survives.

Variety of regimes of starlike networks of Hénon maps.

In this paper we categorize dynamical regimes demonstrated by starlike networks with chaotic nodes. This analysis is done in view of further studying of chaotic scale-free networks, since a starlike structure is the main motif of them. We analyze starlike networks of Hénon maps. They are found to demonstrate a huge diversity of regimes. Varying the coupling strength we reveal chaos, quasiperiodicity, and periodicity. The nodes can be both fully and phase synchronized. The hub node can be either synchronized with the subordinate nodes or oscillate separately from fully synchronized subordinates. There is a range of wild multistability where the zoo of regimes is the most various. One can hardly predict here even a qualitative nature of the expected solution, since each perturbation of the coupling strength or initial conditions results in a new character of dynamics.

Cluster synchronization of starlike networks with normalized Laplacian coupling: master stability function approach

A generalized model of star-like network is suggested that takes into account non-additive coupling and nonlinear transformation of coupling variables. For this model a method of analysis of synchronized cluster stability is developed. Using this method three star-like networks based on Ikeda, predator-prey and Hénon maps are studied.

Faraday effect in alkali-metal vapors in a strong bichromatic field of laser light

Results of a numerical study of the Faraday effect arising upon propagation of the light beams with the frequencies ωL1 (resonant to the nS1/2-nP1/2, 3/2 transitions) and ωL2 (resonant to the nP1/2, 3/2-(n+2)S1/2 transitions) through alkali-metal vapors are presented. Characteristics of the magneto-optical rotation spectra at each of the frequencies are strongly affected by the second intense radiation field resonant to the adjacent transition. When the atoms interact with two strong light waves, resonant to adjacent transitions, and with a magnetic field, the shape of the Faraday rotation spectra depends on the energy shifts of the atomic states that arise due to the dynamic Stark effect and the Zeeman effect (the Paschen-Back or an intermediate-type effect), as well as due to the difference of populations of these states caused by the interaction of the atoms with the fields. The results obtained show that in the frequency selection method, based on the resonance Faraday effect, the frequency of the generated narrow-band beam can be tuned by the intensity of the strong wave, resonant to the transition between the excited states.

Indirect synchronization control in a starlike network of phase oscillators

A starlike network of non-identical phase oscillators is considered that contains the hub and tree rays each having a single node. In such network effect of indirect synchronization control is reported: changing the natural frequency and the coupling strength of one of the peripheral oscillators one can switch on an off the synchronization of the others. The controlling oscillator at that is not synchronized with them and has a frequency that is approximately four time higher then the frequency of the synchronization. The parameter planes showing a corresponding synchronization tongue are represented and time dependencies of phase differences are plotted for points within and outside of the tongue.

Influence of the asymmetry of optical transitions in a three-level atom on the CPT-resonance

The characteristics of CPT-resonance, i.e. its width, depth and contrast, are considered for the three-level Λ-atom interacting with two resonant monochromatic radiation fields. We develop the computer simulation to investigate the influence on these characteristics of the asymmetric properties of medium: inequality of the dipole moments and inequality of the relaxation rates of population. Both weak and strong radiation fields are considered. For the weak fields the inequality of the Rabi-frequencies is found to influence weakly or even not to influence on the CPT-resonance shape. For the strong fields we found the significant influence of the asymmetry on the shape. We conclude that the CPT-resonance in the strong fields can be utilized as a tool for measure of the optical transitions asymmetry. As an example of the real system interacting with two strong radiation fields we consider the characteristics of the CPT-resonance for the magnetic sublevels of states 6P1/2, 6P3/2 and 7S1/2 for Tl-atom.

Numerical analysis of nonlinear resonant polarization phenomena in strong fields

The numerical analyses of polarization phenomena is developed for the radiation fields resonant with the transitions nS1/2-nP1/2,3/2 and nP1/2,3/2 -- (n+2)S1/2 of alkaline atoms. The method of computer simulation of nonlinear resonant polarization phenomena is used, which is based on the solution of the problem of interaction of the real multilevel atom with two laser fields of arbitrary intensity and polarization and with a constant magnetic field. This method is known to be successful applied for the investigation of the polarization phenomena in the atomic gases of the alkaline atoms Na and K. In present paper the whole alkaline group is considered. The represented spectra of rotation of plane of polarization are appear to be qualitatively different for different atoms since atom fine- structure intervals differ very much from each other. The obtained spectra for Rb are in good agreement with the experimental spectra.

Computer analysis of the CPT-dip properties

In our work we develop the computer analysis of the CPT-dip properties. We investigate the dependencies of CPT-dip width, depth and contrast on the radiation fields intensities and detunings, the magnetic fields strength, and the relaxation constants. CPT is observed in the population dynamics of two real three-level atomic systems. One of them is a (Lambda) - type system composed of the magnetic sublevels of 6P1/2, 6P3/2 and 7S1/2 states of Tl atom, the other one is a (Xi) -type system of the magnetic sublevels of 3S1/2, 3P3/2, 5S1/2 states of Na atom. The systems interact with two monochromatic laser fields and magnetic field, which is perpendicular to the laser propagation direction for the lambda-system and parallel for the (Xi) -system. On both cases polarization and mutual configurations of the fields are chosen specific, so that one can select the isolated three- level subsystems in multilevel atomic systems. We observe that the obtained dependencies are different from those in reference 1. It may be explained with non-equal Rabi frequencies and decay rates of neighboring transitions, which are the characteristic feature of real atoms.

Population dynamics for multilevel systems in the external magnetic field

Coherent population trapping effect is widely studied for simple three-level systems of different types ((Xi) , (Lambda) , V). For real atoms situation is more complicated. Atomic levels are degenerated one and in the presence of external fields coupling of magnetic sublevels appears due to as radiation, so magnetic fields, leading to the systems of levels of the higher order. Our theory and model of calculation for interaction of multilevel atom with intense radiation field at the presence of external magnetic field have been applied for considering coherent population trapping effect for such systems.