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.
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.
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.
Swarm theories have become fashionable in theoretical physics over the last decade. They span the range of interactions from individual agents moving in a mean field to coherent collective motions of large agent populations, such as vortex-swarming. But controlled laboratory tests of these theories using real biological agents have been problematic due primarily to poorly known agent-agent interactions (in the case of e.g. bacteria and slime molds) or the large swarm size (e.g. for flocks of birds and schools of fish). Moreover, the entire range of behaviors from single agent interactions to collective vortex motions of the swarm have here-to-fore not been observed with a single animal. We present the results of well defined experiments with the zooplankton Daphnia in light fields showing this range of behaviors. We interpret our results with a theory of the motions of self-propelled agents in a field.
KEYWORDS: Signal to noise ratio, Interference (communication), Stochastic processes, Receptors, Biology, Chaos, Medicine, Sensors, Temperature metrology, Signal processing
Adding random noise to a weak periodic signal can enhance the flow of information through certain nonlinear physical systems, via a process known as stochastic resonance (SR). We have used crayfish mechanoreceptor cells to investigate the possibility that SR can be induced in neurophysiological systems. Various signal-to-noise ratio (SNR) measurements were derived from the action potentials (spikes) of single receptor cells stimulated with weak periodic signals. Spike noise was controlled by one of two methods: (1) adding external noise to the stimulus, or (2) altering internal noise sources by changing the temperature of the cell. In external noise experiments, an optimal noise level can be identified at which the SNR is maximized. In internal noise experiments, although the SNR increases with increasing noise, no SNR maximum has been observed. These results demonstrate that SR can be induced in single neurons, and suggest that neuronal systems may also be capable of exploiting SR.
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