Research Teams
The proposed research programme combines the complementary expertise of the participants in the theory of fluctuations (CO, CR1, CR6, CR8), chaos and chaos control (CR2, CR3, CR5, CR7), synchronisation (CR5, CR7) and its application to the physiology (CR5, CR7), theory of lasers (CR2), the modelling of stochastic and chaotic dynamics (CO, CR1, CR3, CR4, CR5, CR6), experimental nonlinear optics (CR4) and the nonlinear dynamics of the cardiovascular system (CR9).
The research teams have a long-standing interest in the effect of noise
on the dynamics of multistable systems, including chaotic ones. The
proposed programme is based on recent progress achieved by the participants
in this area., and many of the results (see 3.1,
5.2) were
obtained through close collaboration between the scientific teams involved
in the proposed project.
The teams are well set to make a breakthrough in the understanding of the effect of noise on the dynamics of multistable chaotic systems, and to apply this understanding to real physical and physiological systems of topical interest. They have the required expertise to do what is needed and, in particular:
-
to extend the results obtained for non-hyperbolic attractors (CO, CR4, CR5) to the case of fractal boundaries of attraction (T1.1) and, using the expertise of CR3 and CR5, to investigate the influence on the escape process of the evolution of the natural measure in the attractor as a function of time and noise intensity;
-
using the expertise of CR5, to analyse the specific features of the noise-induced escape in quasi-hyperbolic attractors (T.2.1);
-
to extend the analysis of noise-induced transitions in multistable systems (CR1, CR8), and transitions mediated by the presence of homoclinic tangle (CR8, CR1, CR6), to the case of chaotic multistable systems (T3).
A crucial development will be the extension of the technique developed
in the tasks T1 - T3 to the investigations of chaotic maps (T4) using
the expertise of CR2, CR3 and CR5.
The teams can use results of T1 - T4 for the development of new methods
for the control of chaos in multistable systems, combining the methods
of stabilisation and targeting with the energy-optimal control of switching
between attractors. The solution of this problem is distributed between
different tasks and uses the expertise of CO - CR7. The new methods
of control will be applied in T6.
An important extension of their earlier research will be an analysis
of the effect of noise on the synchronisation of coupled chaotic oscillators
(T5). This research will combine the expertise of the CR5 and CR7 in
synchronisation and of CR4, CO, CR6 in the analysis of fluctuational
transitions.
The application of the results obtained to the analysis of stochastic dynamics in semiconductor lasers (T6) and in cardiovascular flow (T7) will be co-ordinated by CR2 and CR9 respectively. At this stage of investigations the combination of expertise of all the participants will be essential. In particular, these applications will require the methods developed in T4 and T5.
|
Team |
Participants |
|
CO: |
Prof. P.V.E. McClintock, Lancaster University, Lancaster, UK |
|
CR1 |
Dr. M. Arrayas, Kamerlingh-Onnes Laboratory, Leiden, The Netherlands |
|
CR2 |
Prof. E.V. Grigorieva, Belarus State University, Minsk, Belarus |
|
CR3 |
Priv.-Doz. Dr. habil. U. Feudel, University of Potsdam, Potsdam,
Germany |
|
CR4 |
Dr. I.Kh. Kaufman, All-Russian Research Institute for Metrological
Service, Moscow, Russia |
|
CR5 |
Dr. I.A. Khovanov, Saratov State University, Saratov, Russia |
|
CR6 |
Dr. R. Mannella, Pisa University, Pisa, Italy |
|
CR7 |
Dr. G. V. Osipov, Nizhny Novgorod University, Nizhny Novgorod,
Russia |
|
CR8 |
Dr. S.M. Soskin, Institute of Semiconductor Physics, Kiev, Ukraine |
|
CR9 |
Prof. A. Stefanovska, University of Ljubljana, Ljubljana, Slovenia |
