A Simple Noise Model with Memory for Biological Systems

A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We find that the time behavior of the illness depends on the noise parameters. Specifically the amplitude and the memory of the noise affect the number of infected people.Comment: 8 pages, 4 figure

Stability in a System subject to Noise with Regulated Periodicity

The stability of a simple dynamical system subject to multiplicative one-side pulse noise with hidden periodicity is investigated both analytically and numerically. The stability analysis is based on the exact result for the characteristic functional of the renewal pulse process. The influence of the memory effects on the stability condition is analyzed for two cases: (i) the dead-time-distorted Poissonian process, and (ii) the renewal process with Pareto distribution. We show that, for fixed noise intensity, the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

Predator population depending on lemming cycles

In this paper, a Langevin equation for predator population with multiplicative correlated noise is analyzed. The noise source, which is a nonnegative random pulse noise with regulated periodicity, corresponds to the prey population cycling. The increase of periodicity of noise affects the average predator density at the stationary state

Stochastic model for the epitaxial growth of two-dimensional islands in the submonolayer regime

The diffusion-based growth of islands composed of clusters of metal atoms on a substrate is considered in the aggregation regime. A stochastic approach is proposed to describe the dynamics of island growth based on a Langevin equation with multiplicative noise. The distribution of island sizes, obtained as a solution of the corresponding Fokker-Planck equation, is derived. The time-dependence of island growth on its fractal dimension is analysed. The effect of mobility of the small islands on the growth of large islands is considered. Numerical simulations are in a good agreement with theoretical results

Development of a Water Bath Electronic Control Unit Based on the Arduino Uno R3

The classical water bath circuit usually uses a thermostat as a temperature regulator to maintain the desired temperature in the compartment. This paper has developed a new PID controller based on the Arduino Uno R3 with application to the water bath to solve the temperature control problem

Environmental Metal Pollution Considered as Noise: Effects on the Spatial Distribution of Benthic Foraminifera in two Coastal Marine Areas of Sicily (Southern Italy)

We analyze the spatial distributions of two groups of benthic foraminifera (Adelosina spp. + Quinqueloculina spp. and Elphidium spp.), along Sicilian coast, and their correlation with six different heavy metals, responsible for the pollution. Samples were collected inside the Gulf of Palermo, which has a high level of pollution due to heavy metals, and along the coast of Lampedusa island (Sicily Channel, Southern Mediterranean), which is characterized by unpolluted sea waters. Because of the environmental pollution we find: (i) an anticorrelated spatial behaviour between the two groups of benthic foraminifera analyzed; (ii) an anticorrelated (correlated) spatial behaviour between the first (second) group of benthic foraminifera with metal concentrations; (iii) an almost uncorrelated spatial behaviour between low concentrations of metals and the first group of foraminifera in clean sea water sites. We introduce a two-species model based on the generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between species and environmental pollution due to the presence in top-soft sediments of heavy metals. The interaction coefficients between the two species are kept constant with values in the coexistence regime. Using proper values for the initial conditions and the model parameters, we find for the two species a theoretical spatial distribution behaviour in a good agreement with the data obtained from the 63 sites analyzed in our study.Comment: 28 pages, 8 figures, 5 table

Ecological Complex Systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noises role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.Comment: 13 pages, Editorial of a topical issue on Ecological Complex System to appear in EPJ B, Vol. 65 (2008

Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator

In this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard system are in a good agreement with the analytical findings