Environmental noise and nonlinear relaxation in biological systems

We investigate the role of the environmental noise in three biological systems: (i) an ecosystem described by a Verhulst model with a multiplicative Lévy noise; (ii) polymer translocation, and (ii) individuals of Nezara viridula. Specifically the transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated as a first biological system. For Cauchy stable noise, exact results for the probability distribution of the population density and nonlinear relaxation are derived. We find a transition induced by the multiplicative Lévy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics, and a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity. (ii) The noise driven translocation of short polymers in crowded solutions is analyzed as a second biological system. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion with a Gaussian uncorrelated and correlated noise source, and an oscillating electric field. We find a nonmonotonic behaviour of the mean first passage time and the most probable translocation time, of the polymer centre of inertia, as a function of the polymer length at low noise intensity: Moreover the mean first translocation time of the polymer centre of inertia shows a resonant activation behavior. Finally we report on experiments on the response of Nezara viridula individuals to sub-threshold signals plus noise in their mating behavior. We analyzed the insect response by directionality tests and different noise intensity levels performed on a group of male individuals. The percentage of insects which react to the sub-threshold signal, shows a non-monotonic behavior, characterized by the presence of a maximum, for increasing levels of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a "soft" threshold model we find that the maximum of the output cross correlation occurs in the same range of noise intensity values for which the activating behavioral has a maximum