Noise-induced escape of periodically modulated systems: from weak to strong modulation

Phase-locked spiking of inner ear hair cells and the driven noisy Adler equation

The inner ear constitutes a remarkably sensitive mechanical detector. This detection occurs in a noisy and highly viscous environment, as the sensory cells-the hair cells-are immersed in a fluid-filled compartment and operate at room or higher temperatures. We model the active motility of hair cell bundles of the vestibular system with the Adler equation, which describes the phase degree of freedom of bundle motion. We explore both analytically and numerically the response of the system to external signals, in the presence of white noise. The theoretical model predicts that hair bundles poised in the quiescent regime can exhibit sporadic spikes-sudden excursions in the position of the bundle. In this spiking regime, the system exhibits stochastic resonance, with the spiking rate peaking at an optimal level of noise. Upon the application of a very weak signal, the spikes occur at a preferential phase of the stimulus cycle. We compare the theoretical predictions of our model to experimental measurements obtained in vitro from individual hair cells. Finally, we show that an array of uncoupled hair cells could provide a sensitive detector that encodes the frequency of the applied signal.

Noise-induced anomalous diffusion over a periodically modulated saddle

We study analytically and numerically the anomalous diffusion across periodically modulated parabolic potential within Langevin and Fokker-Planck descriptions. We find that the probability of particles passing over the saddle is affected strikingly by the periodical modulation with average zero bias. Particularly, the initial phase plays an important role in the modulation effect. The effect of the correlation time of external Ornstein-Uhlenbeck noise on dynamical process is also discussed. A reduction in overpassing probability is observed due to finite correlation time.

Suppression of thermally activated escape by heating

The problem of thermally activated escape over a potential barrier is solved by means of path integrals for one-dimensional reaction dynamics with very general time dependences. For a suitably chosen but still quite simple static potential landscape, the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed constant level.

Phase measurements of barrier crossings in a periodically modulated double-well potential

We report on the experimental observation of the phase angle of a particle escaping over a periodically modulated potential barrier. Optical tweezers and back-focal plane position detection were used to record particle trajectories in the entire double-well potential. These measurements provide a sensitive test of theories proposed in the past decade of escape driven by random thermal noise from a periodically modulated potential. The observed phase shifts as a function of modulation frequency are consistent with those calculated using existing theories.

Pathways of activated escape in periodically modulated systems

We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion-broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed and find their shape. Quantitatively, the tubes are characterized by the distribution of trajectories that, after escape, pass through a given point in phase space for a given modulation phase. This distribution may display several peaks separated by the modulation period. Analytical results agree with the results of simulations of a Brownian particle in a model modulated potential.