Environmental Noise and Nonlinear Relaxation in Biological Systems

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We analyse the effects of environmental noise in three differentbiological systems: (i) mating behaviour of individuals of'Nezara viridula' (L.) (Heteroptera Pentatomidae); (ii) polymer translocation in crowdedsolution; (iii) an ecosystem described by a Verhulst model with amultiplicative Lèvy noise. Specifically, we report onexperiments on the behavioural response of 'N. viridula'individuals to sub-threshold deterministic signals in the presenceof noise. We analyse the insect response by directionality testsperformed on a group of male individuals at different noiseintensities. The percentage of insects which react to thesub-threshold signal shows a non-monotonic behavior, characterizedby the presence of a maximum, for increasing values of the noiseintensity. This is the signature of the non-dynamical stochasticresonance phenomenon. By using a "hard" threshold model we find thatthe maximum of the signal-to-noise ratio occurs in the same rangeof noise intensity values for which the behavioral activation showsa maximum. In the second system, the noise driven translocation ofshort polymers in crowded solutions is analyzed. An improved versionof the Rouse model for a flexible polymer has been adopted to mimicthe molecular dynamics, by taking into account both the interactionsbetween adjacent monomers and introducing a Lennard-Jones potentialbetween non-adjacent beads. A bending recoil torque has also beenincluded in our model. The polymer dynamics is simulated in atwo-dimensional domain by numerically solving the Langevin equationsof motion. Thermal fluctuations are taken into account byintroducing a Gaussian uncorrelated noise. The mean firsttranslocation time of the polymer center of inertia shows a minimumas a function of the frequency of the oscillating forcing field. Inthe third ecosystem, the transient dynamics of the Verhulst modelperturbed by arbitrary non-Gaussian white noise is investigated.Based on the infinitely divisible distribution of the Lèvyprocess we study the nonlinear relaxation of the population densityfor three cases of white non-Gaussian noise: (i) shot noise, (ii)noise with a probability density of increments expressed in terms ofGamma function, and (iii) Cauchy stable noise. We obtain exactresults for the probability distribution of the population densityin all cases, and for Cauchy stable noise the exact expression ofthe nonlinear relaxation time is derived. Moreover starting from aninitial delta function distribution, we find a transition induced bythe multiplicative Lèvy noise, from a trimodal probabilitydistribution to a bimodal probability distribution in asymptotics.Finally we find a nonmonotonic behavior of the nonlinear relaxationtime as a function of the Cauchy stable noise intensity.
Original languageEnglish
Title of host publicationEcological Modeling
Pages289-323
Number of pages35
Publication statusPublished - 2012

Publication series

NameENVIRONMENTAL SCIENCE, ENGINEERING AND TECHNOLOGY

All Science Journal Classification (ASJC) codes

  • General Environmental Science

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