Non-equilibrium distributions at finite noise intensities

We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are in good agreement with the results of numerical solution of the Fokker-Planck equation and Monte Carlo simulations.Comment: 4 pages, 3 figure

Self-consistent analytic solution for the current and the access resistance in open ion channels.

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the currentvoltage characteristics obtained are in good quantitative agreement with experimental measurements

Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.

Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate

Energy-optimal steering of transitions through a fractal basin boundary.

We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states

Charge fluctuations and boundary conditions of biological ion channels:effect on the ionic transition rate

A self-consistent solution is derived for the Poisson-Nernst-Planck (PNP) equation, valid both inside a biological ion channel and in the adjacent bulk fluid. An iterative procedure is used to match the two solutions together at the channel mouth. Charge fluctuations at the mouth are modeled as shot noise flipping the height of the potential barrier at the selectivity site. The resultant estimates of the conductivity of the ion channel are in good agreement with Gramicidin experimental measurements and they reproduce the observed current saturation with increasing concentration

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