Stochastic chaos: An analog of quantum chaos

Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger equation, can exhibit a transition in their spectral statistics as a coupling parameter is varied. This transition is connected to the transition to non-integrability in the Hamilton's equations.Comment: Uuencoded compressed postscript file, 4 pages, 3 fig

Trans-membrane Signal Transduction and Biochemical Turing Pattern Formation

The Turing mechanism for the production of a broken spatial symmetry in an initially homogeneous system of reacting and diffusing substances has attracted much interest as a potential model for certain aspects of morphogenesis such as pre-patterning in the embryo, and has also served as a model for self-organization in more generic systems. The two features necessary for the formation of Turing patterns are short-range autocatalysis and long-range inhibition which usually only occur when the diffusion rate of the inhibitor is significantly greater than that of the activator. This observation has sometimes been used to cast doubt on applicability of the Turing mechanism to cellular patterning since many messenger molecules that diffuse between cells do so at more-or-less similar rates. Here we show that stationary, symmetry-breaking Turing patterns can form in physiologically realistic systems even when the extracellular diffusion coefficients are equal; the kinetic properties of the 'receiver' and 'transmitter' proteins responsible for signal transduction will be primary factors governing this process

Temporally Asymmetric Fluctuations are Sufficient for the Operation of a Correlation Ratchet

It has been shown that the combination of a broken spatial symmetry in the potential (or ratchet potential) and time correlations in the driving are crucial, and enough to allow transformation of the fluctuations into work. The required broken spatial symmetry implies a specific molecular arrangement of the proteins involved. Here we show that a broken spatial symmetry is not required, and that temporally asymmetric fluctuations (with mean zero) can be used to do work, even when the ratchet potential is completely symmetric. Temporal asymmetry, defined as a lack of invariance of the statistical properties under the operation to temporal inversion, is a generic property of nonequilibrium fluctuation, and should therefore be expected to be quite common in biological systems.Comment: 17 pages, ps figures on request, LaTeX Article Forma

Recovering ‘lost’ information in the presence of noise: application to rodent–predator dynamics.

A Hamiltonian approach is introduced for the reconstruction of trajectories and models of complex stochastic dynamics from noisy measurements. The method converges even when entire trajectory components are unobservable and the parameters are unknown. It is applied to reconstruct nonlinear models of rodent–predator oscillations in Finnish Lapland and high-Arctic tundra. The projected character of noisy incomplete measurements is revealed and shown to result in a degeneracy of the likelihood function within certain null-spaces. The performance of the method is compared with that of the conventional Markov chain Monte Carlo (MCMC) technique

Rectification of Fluctuations in an Underdamped Ratchet

We investigate analytically the motion of underdamped particles subject to a deterministic periodic potential and a periodic temperature. Despite the fact that an underamped particle experiences the temperature oscillation many times in its escape out of a well and in its motion along the potential, a net directed current linear in the friction constant is found. If both the potential and the temperature modulation are sinusoidal with a phase lag $\delta$, this current is proportional to $\sin \delta$.Comment: 4 pages REVTEX, 2 figures include

Applications of dynamical inference to the analysis of noisy biological time series with hidden dynamical variables.

We present a Bayesian framework for parameter inference in noisy, non-stationary, nonlinear, dynamical systems. The technique is implemented in two distinct ways: (i) Lightweight implementation: to be used for on-line analysis, allowing multiple parameter estimation, optimal compensation for dynamical noise, and reconstruction by integration of the hidden dynamical variables, but with some limitations on how the noise appears in the dynamics; (ii) Full scale implementation: of the technique with extensive numerical simulations (MCMC), allowing for more sophisticated reconstruction of hidden dynamical trajectories and dealing better with sources of noise external to the dynamics (measurements noise)

Cooperative Transport of Brownian Particles

We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.Comment: 4 pages, 5 figure

Directed transport of Brownian particles in a double symmetric potential

We investigate the dynamics of Brownian particles in internal state- dependent symmetric and periodic potentials. Although no space or time symmetry of the Hamiltonian is broken, we show that directed transport can appear. We demonstrate that the directed motion is induced by breaking the symmetry of the transition rates between the potentials when these are spatially shifted. Finally, we discuss the possibility of realizing our model in a system of cold particles trapped in optical lattices.Comment: to appear in Physical Review

Asymmetric motion in a double-well under the action of zero-mean Gaussian white noise and periodic forcing

Residence times of a particle in both the wells of a double-well system, under the action of zero-mean Gaussian white noise and zero-averaged but temporally asymmetric periodic forcings, are recorded in a numerical simulation. The difference between the relative mean residence times in the two wells shows monotonic variation as a function of asymmetry in the periodic forcing and for a given asymmetry the difference becomes largest at an optimum value of the noise strength. Moreover, the passages from one well to the other become less synchronous at small noise strength as the asymmetry parameter (defined below) differs from zero, but at relatively larger noise strengths the passages become more synchronous with asymmetry in the field sweep. We propose that asymmetric periodic forcing (with zero mean) could provide a simple but sensible physical model for unidirectional motion in a symmetric periodic system aided by a symmetric Gaussian white noise.Comment: Appeared in PRE March 1997, figures available on reques