Tatiana Vadivasova
Publications:
Shepelev I. A., Vadivasova T. E.
Solitary states in a 2D lattice of bistable elements with global and close to global interaction
2017, Vol. 13, No. 3, pp. 317329
Abstract
This paper is concerned with the spatiotemporal dynamics of the 2D lattice of cubic maps with
nonlocal coupling. Different types of chimera structures have been found. Also, the underexplored
regime of solitary states has been found. It is shown that the solitary states are typical of a large
coupling radius. The possibility of detecting such a regime increases with the transition to global
interaction, while chimera states disappear.

Shepelev I. A., Vadivasova T. E.
Chimera regimes in a ring of elements with local unidirectional interaction
2016, Vol. 12, No. 2, pp. 197209
Abstract
Complex spatial structures, called chimeras, are the subject of considerable recent interest. They consist of stationary areas with coherent and incoherent behavior of neighboring elements. A number of problems related to similar structures have not been solved yet. One of these problems concerns the element interaction in ensembles, when stable chimera structures can be observed. Until quite recently it was assumed that one of the most important conditions for the existence of chimeras is the nonlocal character of interaction. However, this assumption is not exactly correct. Chimeras can be realized for special types of local coupling. So, the chimera examples were obtained in ensembles with inertial local coupling. The additional variable is introduced for a coupling specification. It is given by a linear differential equation. Also, the socalled virtual chimeras exist in oscillators with delayed feedback. This allows one to assume that chimera states can be obtained in a ring of local coupling oscillators with unidirectional interaction, which is inertialess, but has a nonlinear character. This assumption is based on a qualitative similarity between the behaviors of an oscillator with delay feedback and a ring of the same oscillators with local unidirectional coupling. The basis of this work is the system with delay feedback, which demonstrates the existence of a virtual chimera. The distributed analog is investigated. It is an oscillator ring with unidirectional nonlinear local coupling. The existence of chimera structures in the ring were found in the special area of parameter changing via computing simulation. This chimera moves in a ring with constant velocity and is similar to the chimera in the system with delay feedback. The area of chimera existence of parameter variations was studied. Regime diagrams were plotted on the plane of control parameters. The scenario of chimera destruction for the coupling increase was shown. 
Semenov V. V., Zakoretskii K. V., Vadivasova T. E.
Experimental investigation of stochastic Andronov–Hopf bifurcation in selfsustained oscillators with additive and parametric noise
2013, Vol. 9, No. 3, pp. 421434
Abstract
Effects of noisy influence on oscillators near oscillation threshold are studied by means of numerical simulation and natural experiments. Two qualitative different models (Van derPol and Anishchenko—Astakhov selfsustained oscillators) are considered. Evolution laws of probabilistic distribution with increase of noise intensity are established for two cases: addition of additive and parametric white gaussian noise in researched systems. It is shown that the noise destroys the distribution form, which is typical for selfoscillations, that leads to shift of bifurcation to direction of excitation parameter increase. The existence of bifurcation interval, which corresponds with gradual transition to regime of selfoscillation, was detected from experiments with additive noise.

Slepnev A. V., Vadivasova T. E.
Two kinds of autooscillations in active medium with periodical border conditions
2012, Vol. 8, No. 3, pp. 497505
Abstract
The model of an active medium with periodical boundary conditions is studied. The elementary cell is chosen to be FitzHugh–Nagumo oscillator. According to the values of parameters the elementary cell is able to be either in selfsustained regime or in excitable one. In both cases there are sustained oscillations in each elementary cell of the medium, but the causes of its initiation are different. In case of the former each cell in itself is autooscillator, in case of the latter the oscillations appear because of feedback which is provided by the periodical boundary conditions. In both cases the phenomenon of multistability is observed. The comparative analysis of the regimes mentioned above is carried out. There are shown that the dependencies of oscillations characteristics from the system parameters in either cases significantly differ from one another. The bifurcational type of the transition from one cell regime to another is ascertained for some modes. The influence of spatialuncorrelated noise on the active medium behavior is considered. The average period of oscillations versus noise intensity relation is obtained.

Slepnev A. V., Vadivasova T. E., Listov A. S.
Multistability, period doubling and traveling waves suppression by noise excitation in a nonlinear selfoscillatory medium with periodic boundary conditions
2010, Vol. 6, No. 4, pp. 755767
Abstract
The model of a selfoscillatory medium whose cells represent AnishchenkoAstakhov selfsustained oscillators is studied. Under periodic boundary conditions the phenomenon of multistability is observed in the medium — the stable selfsustained oscillatory modes with different spatial structures coexist and can be realized by means of appropriately chosen initial conditions. The study of the time period doubling bifurcations is performed for different modes. It is shown that the evolution of the modes between two successive bifurcations leads to the complexification of instantaneous spatial profile and to the appearance of smallscale spatial oscillations. The distribution of the instantaneous phase shift along the medium is studied in different regimes. The influence of local noise source on the spatial structures is considered. It is demonstrated that noise can induce switchings between different regimes. The mechanism of such switchings is explored.

Malyaev V. S., Vadivasova T. E.
Parameter estimation in dynamical systems with additive noise
2010, Vol. 6, No. 2, pp. 267276
Abstract
In the present paper possibilities of parameters estimation are considered in dynamical systems (DS) with additive noise. Simple and effective algorithms, optimal parameter values of numeric simulation and data filtration methods are proposed that enable one to find the controlling parameter value of a noisy DS with a high accuracy. Different DS are studied, and the accuracy of parameter estimation is examined for various dynamical modes and for different noise intensities.

Anishchenko V. S., Vadivasova T. E., Strelkova G. I.
Selfsustained oscillations of dynamical and stochastic systems and their mathematical image — an attractor
2010, Vol. 6, No. 1, pp. 107126
Abstract
In the present paper autonomous and nonautonomous oscillations of dynamical and stochastic systems are analyzed in the framework of common concepts. The definition of an attractor is introduced for a nonautonomous system. The definitions of selfsustained oscillations and a selfsustained oscillatory system is proposed, that generalize A.A.Andronov’s concept introduced for autonomous systems with one degree of freedom.

Anishchenko V. S., Astakhov S. V., Vadivasova T. E., Feoktistov A. V.
Numerical and experimental study of external synchronization of twofrequency oscillations
2009, Vol. 5, No. 2, pp. 237252
Abstract
The effect of synchonization has been studied in a system of two coupled Van der Pol oscillators under external harmonic force. The bifurcation analysis has been carried out using the phase approach. The mechanisms of complete and partial synchronization have been established. The main type of bifurcation described in the paper is the saddlenode bifurcation of invariant curves that corresponds to the saddlenode bifurcation of twodimensional tori in the complete system of differential equations for the dynamical system under study. We illustrate the bifurcational mechanisms obtained from numerical experiment by the results of physical experiment. The synchronization phenomenon in the vicinity of resonances on a torus with winding numbers 1 : 1 and 1 : 3 is considered in the physical experiment.

Zakharova A. S., Vadivasova T. E., Anishchenko V. S.
The interconnection of synchronization threshold with effective diffusion coefficient of instantaneous phase of chaotic selfsustained oscillations
2008, Vol. 4, No. 2, pp. 160180
Abstract
We investigate effective diffusion coefficient of instantaneous phase of chaotic selfsustained oscillations and its connection with synchronization threshold. It is showed that effective phase diffusion coefficient in contrast to maximal Lyapunov exponent allows to distinguish the regions of spiral and funnel attractor. We ascertain that synchronization threshold of chaos is in orderofmagnitude agreement with the value of diffusion coefficient divided by the mean frequency of selfsustained oscillations.
