Activities

TEACHING EXPERIENCE

The Lecture topics:  Foundations of general physics (2000– 2001)

My basic activities refer to the field of nonlinear dynamics and chaos. Especially the chaos suppression and synchronization of chaotic behavior was the main aim of my recent scientific research. I performed spectral analysis of the various time series ranging from the data of numerical experiments of model chaotic systems to the time series of the real cardiac measurements. In my work I
combine numerical and analytical methods.

Among my main achievements in analytical studies of the nonlinear dynamics are:

I developed a new method of finding the necessary properties of the external perturbation, which should synchronize the chaotic
dynamics. The new method has been successfully tested in application to the model system
Duffing-Holmes oscillator and classical nonlinear pendulum with dissipation.
The main results on these topics are in the following publications:

This method has an important advantage of being a "soft" way synchronization in chaotic systems as compared to the standard methods of parametric control. I developed a theoretical approach which justifies the above practical method and proved a theorem which reveals that the above method is a consequence of basic properties of chaotic systems, that "Dynamical systems with homoclinical and heteroclinical chaos which posses the stabilizing perturbation are topological equivalent to a wide class of regular systems"

This theorem predicts that one can elaborate many (infinite number, strictly speaking) methods of synchronization; it also shows the way how these methods could be elaborated.

Presently I am working on the extension of the method, developed in my previous studies in the application to the continuous
systems and three-body problem. In particular to the continuous excitable media in application to the modelling of the cardiac tissues. As regards the three-body problem I am studying and modelling of chaotic behavior in application to the planetary
rings. On of my present activities refers to the elaboration of a set of programs addressed to modelling and data analysis of
three-body system and continuous excitable system with chaotic behavior.

The main results on these topics are in the following publications:

Publications

1. A.Loskutov, A.Dzhanoev Chaos Suppression in separatrix neighborhood. // Sov.Phys. JETP, 2004, Vol.125. No4. pp. 191-200.2

2. A.Loskutov and A.Dzhanoev "General mechanism for suppression of homoclinic chaos" // In: The Book of Abstracts of 12-th International IEEE Workshop Nonlinear Dynamics of Electronic Systems, NDES 2004,pp.56--60, Portugal, 9-13 May 2004.

3. A.Dzhanoev and A.Loskutov The main mechanism of homoclinic chaos suppression. // In: The Book of Abstracts of VII International School--Conference ``CHAOS'2004'', pp.43--44, Saratov, Russia, 1--6 October 2004.

4. A.Loskutov, A.Dzhanoev Stabilization of the Chaotic Behavior of Dynamical Systems. // Doklady Physics (Reports of Russian Academe of Sciences, Doklady RAN), Vol.48, No.10, 2003, pp. 481-4833.

5. A.Loskutov, A.Dzhanoev Homoclinical Structures and Chaos Phenomena. // In: The Book of Abstracts of the 6th Int. Conf. on
''Computing Anticipatory Systems''(CASYS'03), Liege, Belgium, 11-16 August, 2003.

6. A.Loskutov and A.Dzhanoev. Homoclinical Chaos Suppression. // In: Proc. of 2003 Int. Conf. ''Physics and Control''(PhysCon'03), 20-22 August, Saint Petersburg, Russia. Eds. A.L.Fradkov and A.N.Churilov.-IEEE, p.403-409.4, 2003.

7. A.Loskutov and A.Dzhanoev. Chaos Suppression in Homoclinical Structures. // In: Nonlinear Dynamics and control . Issue 3: Collected papers/Eds S.V.Emelyanov, S.K.Korovin.--M.:FIZMATLIT, p.107-123, 2003.

8. A.Loskutov and A.Dzhanoev. Homoclinical Chaos Suppression. // In: The Book of Abstracts of the XXXI Summer School-Conference ''Advanced Problems in Mechanics'',p.67, Saint Petersburg, June 22-July 2 2003.

9. A.Loskutov and A.Dzhanoev. Application of the Melnikov method to the investigation of complex behavior. // In: The Book of Abstracts of the 4th Int. Symp. ''Mobility in Polymer Systems'', p.226, St. Petersburg, 3-7 June 2002.

10.T.Schwalger, A.Loskutov and A.Dzhanoev "May chaos always be suppressed?" // In print.