We propose a model for a walker moving on an asymmetric periodic ratchet potential. The walker has two 'feet' represented as two finite-size particles coupled nonlinearly through a double-well potential. In contrast to linear coupling, the bistable potential admits a richer dynamics where the ordering of the particles can alternate. The transitions between the two stable points on the bistable potential, correspond to a walking with alternating particles. In our model, each particle is acted upon by independent white noises, modeling thermal noise, and additionally we have an external time-dependent force that drives the system out of equilibrium, allowing directed transport. This force can be common colored noise, periodic deterministic driving or fluctuations on the bistable potential. In the equilibrium case, where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns available for various parameter settings. Numerical simulations showed the existence of current reversals and significant changes in the effective diffusion constant and in the synchronization index. We obtained an optimal coherent transport, characterized by a maximum dimensionless ratio of the current and the effective diffusion (Peclet number), when the periodicity of the ratchet potential coincides with the equilibrium distance between the two particles.
Random processes acting through dynamical systems with thresholds lie at the heart of many natural and man-made phenomena. The thresholds here considered are general including not only sharp or “hard” boundaries but also a class of dynamical, nonlinear system functions some of which are themselves mediated by the noise. Processes include noise-induced transitions, postponed and advanced bifurcations, noise enhanced propagation of coherent structures, and stochastic resonance and synchronization. Examples of these processes are found in a wide range of disciplines from physics and chemistry to neuroscience and even human and animal behavior and perception. I will discuss some of these examples connecting them with their fundamental dynamical origins.
Classical notion of synchronization, introduced originally for periodical self-sustained oscillators, can be extended to stochastic systems. This can be done even in the case when the characteristic times of a system are fully controlled by noise. Stochastic synchronization is then defined by imposing certain conditions to various statistical measures of the process. We review various approaches to stochastic synchronization and apply them to study synchronization in the electrosensory system of paddlefish.
We demonstrate the existence of two types of oscillators embedded in the electroreceptor system of paddlefish. The first type of oscillator is represented by the collective activity of hundreds of epithelial cells. It produces stochastic oscillations with a well-expressed peak in the power spectrum at approx. 25 Hz. The second oscillator resides in the afferent terminals and is driven by the first, epithelial oscillations. We show that the existence of the epithelial oscillation leads to two main effects. On the one hand, it busts variability of afferent firing, expressed as an increase of the coefficient of variation of interspike intervals. On the other hand, however, the epithelial oscillations involve additional degree of ordering expressed in the extended negative correlations between sequential interspike intervals. We discuss implications of extended negative correlations on the performance of electroreceptors.
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