Environmental noise and nonlinear relaxation in biological systems

Dubkov, Aa

Research output: Other contribution

Abstract

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.
Original languageEnglish
Publication statusPublished - 2009

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noise intensity
polymers
insects
inertia
thresholds
ecosystems
white noise
low noise
cross correlation
equations of motion
relaxation time
signatures
activation
electric fields
output

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Environmental noise and nonlinear relaxation in biological systems. / Dubkov, Aa.

2009, .

Research output: Other contribution

@misc{c6e542bc7679475d9ff3b982ed0c7ce1,
title = "Environmental noise and nonlinear relaxation in biological systems",
abstract = "We investigate the role of the environmental noise in three biological systems: (i) an ecosystem described by a Verhulst model with a multiplicative L{\'e}vy 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 L{\'e}vy 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.",
keywords = "Biological systems; Levy Noise; Polymer translocation; Environmental noise",
author = "{Dubkov, Aa} and {La Cognata}, Angelo and Bernardo Spagnolo and Stefano Colazza and Pasquale Caldara and Stefano Spezia and Davide Valenti and Nicola Pizzolato and {Lo Bue}, Paolo and Ezio Peri and Alessandro Fiasconaro and Luciano Curcio",
year = "2009",
language = "English",
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TY - GEN

T1 - Environmental noise and nonlinear relaxation in biological systems

AU - Dubkov, Aa

AU - La Cognata, Angelo

AU - Spagnolo, Bernardo

AU - Colazza, Stefano

AU - Caldara, Pasquale

AU - Spezia, Stefano

AU - Valenti, Davide

AU - Pizzolato, Nicola

AU - Lo Bue, Paolo

AU - Peri, Ezio

AU - Fiasconaro, Alessandro

AU - Curcio, Luciano

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Biological systems; Levy Noise; Polymer translocation; Environmental noise

UR - http://hdl.handle.net/10447/50192

M3 - Other contribution

ER -