A. N. Silchenko

Quasiadiabatic decay of capillary turbulence on the charged surface of liquid hydrogen.

We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that decay begins from the high frequency end of the spectral range, while most of the energy remains localized at low frequencies. The apparent discrepancy with the self-similar theory of nonstationary wave turbulent processes is accounted for in terms of a quasiadiabatic decay wherein fast nonlinear wave interactions redistribute energy between frequency scales in the presence of finite damping at all frequencies. Numerical calculations based on this idea agree well with experimental data.

Fluctuational Transitions through a Fractal Basin Boundary.

Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of homoclinic points. The most probable escape path from the chaotic attractor to the fractal boundary is found using both statistical analyses of fluctuational trajectories and the Hamiltonian theory of fluctuations.

Noise-induced escape through a fractal basin boundary

We study noise-induced escape within a discrete dynamical system that has two co-existing chaotic attractors in phase space separated by a locally disconnected fractal basin boundary. It is shown that escape occurs via a unique accessible point on the fractal boundary. The structure of escape paths is determined by the original saddles forming the homoclinic structure of the system and by their hierarchical interrelations.

MID-INFRARED LASING INDUCED BY NOISE

We demonstrate that external noise can play a constructive role in a laser diode, inducing coherent mid-infrared radiation. Depending on noise intensity, the induced lasing can be either unimode or mulitimode. The coherence of the radiation in each mode reaches its maximum at an optimal noise intensity that differs depending on the mode. The phenomenon can therefore be classified as a multiple coherence resonance.

Fluctuational escape from chaotic attractors in multistable systems

Recent progress towards an understanding of fluctuational escape from chaotic attractors (CAs) is reviewed and discussed in the contexts of both continuous systems and maps. It is shown that, like the simpler case of escape from a regular attractor, a unique most probable escape path (MPEP) is followed from a CA to the boundary of its basin of attraction. This remains true even where the boundary structure is fractal. The importance of the boundary conditions on the attractor is emphasized. It seems that a generic feature of the escape path is that it passes via certain unstable periodic orbits. The problems still remaining to be solved are identified and considered.

Energy-optimal steering of transitions through a fractal basin boundary

We study fluctuational transitions in a discrete dynamical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique accessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original saddles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctuational force obtained from a numerical analysis of the fluctuational transitions between two states.

Solution of the boundary value problem for nonlinear flows and maps

Fluctuational escape via an unstable limit cycle is investigated in stochastic flows and maps. A new topological method is suggested for analysis of the corresponding boundary value problems when the action functional has multiple local minima along the escape trajectories and the search for the global minimum is otherwise impossible. The method is applied to the analysis of the escape problem in the inverted Van der Pol oscillator and in the Henon map. An application of this technique to solution of the escape problem in chaotic maps with fractal boundaries, and in maps with chaotic saddles embedded within the basin of attraction, is discussed.

Fluctuational Escape from Chaotic Attractors

Noise-induced escape from a non-hyperbolic attractor, and from a quasihyperbolic attractor with nonfractal boundaries, is investigated by means of analogue experiments and numerical simulations. It is found that there exists a most probable (optimal) escape trajectory, the prehistory of the escape being defined by the structure of the chaotic attractor. The corresponding optimal fluctuational force is found. The possibility of achieving analytic estimates of the escape probability within the framework of Hamiltonian formalism is discussed.

Escape from a chaotic attractor with fractal basin boundaries

We study fluctuational transitions in a discrete dynamical system between two co-existing chaotic attractors separated by a fractal basin boundary. It is shown that there is a generic mechanism of fluctuational transition through a fractal boundary determined by a hierarchy of homoclinic original saddles. The most probable escape path from a chaotic attractors to the fractal boundary is found using both statistical analysis of fluctuational trajectories and Hamiltonian theory of fluctuations.