Related papers: Nonequilibrium limit cycle oscillators: fluctuatio…
Under general conditions imposed on an active stochastic oscillator, we study change in the size and shape of its average limit cycle as a function of temperature. Such dynamics occur in a multitude of nonequilibrium systems, including the…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong violation of the…
The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a stochastic, nonlinear oscillator driven by internal active processes. Moreover, this internal activity is adaptive -- its power input depends on…
We consider a purely harmonic chain of oscillators which is perturbed by a stochastic noise. Under this perturbation, the system exhibits two conserved quantities: the volume and the energy. At the level of the hydrodynamic limit, under…
Hair cells of the auditory and vestibular systems display astonishing sensitivity, frequency selectivity, and temporal resolution to external signals. These specialized cells utilize an internal active amplifier to achieve highly sensitive…
Hair cells of the auditory and vestibular systems are capable of detecting sounds that induce sub-nanometer vibrations of the hair bundle, below the stochastic noise levels of the surrounding fluid. Hair bundles of certain species are also…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
Many physical and biological systems exhibit intrinsic cyclic dynamics that are altered by random external perturbations. We examine continuous-time autonomous dynamical systems exhibiting a stable limit cycle, perturbed by additive…
Sensory hair cells in auditory and vestibular organs rely on active mechanisms to achieve high sensitivity and frequency selectivity. Recent experimental studies have documented self-sustained oscillations in hair cells of lower vertebrates…
Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various…
We introduce the concept of self-tuned criticality as a general mechanism for signal detection in sensory systems. In the case of hearing, we argue that active amplification of faint sounds is provided by a dynamical system which is…
The hair cells of the vertebrate inner ear convert mechanical stimuli to electrical signals. Two adaptation mechanisms are known to modify the ionic current flowing through the transduction channels of the hair bundles: a rapid process…
Modelling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
Overdamped stochastic systems maintained far from equilibrium can display sustained oscillations with fluctuations that decrease with the system size. The correlation time of such noisy limit cycles expressed in units of the cycle period is…
Experimental records of active bundle motility are used to demonstrate the presence of a low-dimensional chaotic attractor in hair cell dynamics. Dimensionality tests from dynamic systems theory are applied to estimate the number of…
Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the…
Rhythmic fluctuations in acoustic energy and accompanying neuronal excitations in cortical oscillations are characteristic of human speech, yet whether a corresponding rhythmicity inheres in the articulatory movements that generate speech…