A. G. Balanov

Delayed Feedback as a Means of Control of Noise-Induced Motion

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.

Bifurcation analysis of a neutral delay differential equation modelling the torsional motion of a driven drill-string

Using techniques from dynamical systems analysis we explore numerically the solution space, under parametric variation, of a neutral differential delay equation that arises naturally in the Cosserat description of torsional waves on a driven drill-string.

Controlling and enhancing terahertz collective electron dynamics in superlattices by chaos-assisted miniband transport

We show that a tilted magnetic field transforms the structure and THz dynamics of charge domains in a biased semiconductor superlattice. At critical field values, strong coupling between the Bloch and cyclotron motion of a miniband electron triggers chaotic delocalization of the electron orbits, causing strong resonant enhancement of their drift velocity. This dramatically affects the collective electron behavior by inducing multiple propagating charge domains and GHz-THz current oscillations with frequencies ten times higher than with no tilted field.

ENTRAINMENT BETWEEN HEART RATE AND WEAK NONINVASIVE FORCING

We demonstrate that the heart rate of a healthy human can be synchronized by means of weak external noninvasive forcing in the form of a sequence of sound and light pulses, being either periodic or aperiodic, the latter forcing given by interbeat intervals of the heart of another subject. The phenomenon of phase locking of n:m type is observed for both situations in about 90% of our experiments. The plot for the ratio of forcing frequency to the average frequency of response versus detuning possesses a plateau and is in agreement with classical synchronization theory.

Effect of temperature on resonant electron transport through stochastic conduction channels in superlattices

We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localized to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric-field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between the thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency.

Role of multistability in the transition to chaotic phase synchronization

In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples using Rossler systems and model maps are given. (c) 1999 American Institute of Physics.

CONTROLLING STOCHASTIC OSCILLATIONS CLOSE TO A HOPF BIFURCATION BY TIME-DELAYED FEEDBACK

We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.

Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.

SYNCHRONIZATION IN DRIVEN CHAOTIC SYSTEMS : DIAGNOSTICS AND BIFURCATIONS

Abstract We investigate generic aspects of chaos synchronization in an externally forced Rossler system. By comparing different diagnostic methods, we show the existence of a well-defined cut-off of synchronization associated with the transition from weak to fully developed chaos. Chaotic synchronization is found to be lost at this cut-off only after the last band-merging bifurcation has occurred. Everywhere at the boundary of phase synchronization, one of the Lyapunov exponents becomes equal to zero. Two types of chaotic behavior, differing by the number of vanishing Lyapunov exponents, are observed outside the synchronization region.

Controlling high-frequency collective electron dynamics via single-particle complexity

We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.