Noise Induced Phenomena in the Dynamics of Two Competing Species

Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise delayed extinction, and noise induced pattern formation. In addition, our theoretical results are validated with experimental findings. Specifically the results, obtained by a coupled map lattice model, well reproduce the spatial distributions of anchovies and sardines, observed in a marine ecosystem. Moreover, the experimental dynamical behavior of two competing bacterial populations in a meat product and the probability distribution at long times of one of them are well reproduced by a stochastic microbial predictive model.Comment: 23 pages, 8 figures; to be published in Math. Model. Nat. Phenom. (2016

Strong cosmic censorship and Misner spacetime

Misner spacetime is among the simplest solutions of Einstein's equation that exhibits a Cauchy horizon with a smooth extension beyond it. Besides violating strong cosmic censorship, this extension contains closed timelike curves. We analyze the stability of the Cauchy horizon and prove that neighboring spacetimes in one parameter families of solutions through Misner's in pure gravity, gravity coupled to a scalar field, or Einstein-Maxwell theory end at the Cauchy horizon developing a curvature singularity.publishedVersionFil: Denaro, Pedro Ignacio Esteban. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Denaro, Pedro Ignacio Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina.Fil: Dotti, Gustavo Daniel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Dotti, Gustavo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina.Otras Ciencias Física

A systematic review of single-bundle versus double-bundle anterior cruciate ligament reconstruction

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Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion Model

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values

STOCHASTIC DYNAMICS OF TWO PICOPHYTOPLANKTON POPULATIONS IN A REAL MARINE ECOSYSTEM

A stochastic reaction-diffusion-taxis model is analyzed to get the stationary distribution along water column of two species of picophytoplankton, that is picoeukaryotes and Prochlorococcus. The model is valid for weakly mixed waters, typical of the Mediterranean Sea. External random fluctuations are considered by adding a multiplicative Gaussian noise to the dynamical equation of the nutrient concentration. The statistical tests show that shape and magnitude of the theoretical concentration profile exhibit a good agreement with the experimental findings. Finally, we study the effects of seasonal variations on picophytoplankton groups, including an oscillating term in the auxiliary equation for the light intensity

Spatio-temporal dynamics of a planktonic system and chlorophyll distribution in a 2D spatial domain: matching model and data

Field data on chlorophyll distribution are investigated in a two-dimensional spatial domain of the Mediterranean Sea by using for phytoplankton abundances an advection-diffusion-reaction model, which includes real values for physical and biological variables. The study exploits indeed hydrological and nutrients data acquired in situ, and includes intraspecific competition for limiting factors, i.e. light intensity and phosphate concentration. As a result, the model allows to analyze how both the velocity field of marine currents and the two components of turbulent diffusivity affect the spatial distributions of phytoplankton abundances in the Modified Atlantic Water, the upper layer of the water column of the Mediterranean Sea. Specifically, the spatio-temporal dynamics of four phytoplankton populations, responsible for about 80% of the total chlorophyll a, are reproduced. Results for phytoplankton abundances obtained by the model are converted in chlorophyll a concentrations and compared with field data collected in twelve marine sites along the Cape Passero (Sicily)- Misurata (Libya) transect. Statistical checks indicate a good agreement between theoretical and experimental distributions of chlorophyll concentration. The study can be extended to predict the spatio-temporal behaviour of the primary production, and to prevent the consequent decline of some fish species in the Mediterranean Sea

Modeling of Sensory Characteristics Based on the Growth of Food Spoilage Bacteria

During last years theoretical works shed new light and proposed new hypothesis on the mechanisms which regulate the time behaviour of biological populations in different natural systems. Despite of this, a relevant physical and biological issue such as the role of environmental variables in ecological systems is still an open question. Filling this gap of knowledge is a crucial task for a deeper comprehension of the dynamics of biological populations in real ecosystems. The aim of this work is to study how dynamics of food spoilage bacteria influences the sensory characteristics of fresh fish specimens. This topic is worth of investigation in view of a better understanding of the role played by the bacterial growth on the organoleptic properties, and becomes crucial in the context of quality evaluation and risk assessment of food products. We therefore analyze and reproduce the time behaviour, in fresh fish specimens, of sensory characteristics starting from the growth curves of two spoilage bacterial communities. The theoretical study, initially based on a deterministic model, is performed by using the temperature profiles obtained during the experimental analysis. As a first step, a model of predictive microbiology is used to reproduce the experimental behaviour of the two bacterial populations. Afterwards, the theoretical bacterial growths are converted, through suitable differential equations, into "sensory" scores, based on the Quality Index Method (QIM), a scoring system for freshness and quality sensory estimation of fishery products. As a third step, the theoretical curves of QIM scores are compared with the experimental data obtained by sensory analysis. Finally, the differential equations for QIM scores are modified by adding terms of multiplicative white noise, which mimics the effects of uncertainty and variability in sensory analysis. A better agreement between experimental and theoretical QIM scores is observed, in some cases, in the presence of suitable values of noise intensity respect to the deterministic analysis

The role of noise on the steady state distributions of phytoplankton populations

The spatio-temporal behaviour of total chlorophyll concentration is investigated in the middle of the Tyrrhenian Sea by using a stochastic approach. The study is based on a reaction-diffusion-taxis model, which is used to analyse the dynamics of five phytoplankton groups, responsible for about 80% of the total chlorophyll a inside the euphotic zone of the water column. The analysis is performed by considering: (i) the intraspecific competition of the phytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration, (ii) the seasonal changes of environmental variables, and (iii) the random fluctuations of the components of the velocity field and temperature. Specifically, we investigate the effects of external perturbations, both deterministic and random, on the dynamics of phytoplankton populations, by inserting a term of multiplicative noise into the differential equation of the nutrient dynamics. The theoretical results of the phytoplankton abundances obtained by the stochastic model are converted in chlorophyll a concentrations, and compared with the experimental findings. The statistical checks, based on the chi-square test, show that the vertical distributions of total chlorophyll concentration are in a good agreement with the experimental data. Finally, we observe that the high intensity of environmental noise strongly modifies the steady spatial distributions of two phytoplankton groups usually localized in deeper layers, causing algal blooms in surface water

Stochastic models for phytoplankton dynamics in Mediterranean Sea

In this paper, we review some results obtained from three one-dimensional stochastic models, which were used to analyze picophytoplankton dynamics in two sites of the Mediterranean Sea. Firstly, we present a stochastic advection\u2013reaction\u2013diffusion model to describe the vertical spatial distribution of picoeukaryotes in a site of the Sicily Channel. The second model, which is an extended version of the first one, is used to obtain the vertical stationary profiles of two groups of picophytoplankton, i.e. Pelagophytes and Prochlorococcus, in the same marine site as in the previous case. Here, we include intraspecific competition of picophytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration. Finally, we analyze the spatio-temporal behaviour of five picophytoplankton populations in a site of the Tyrrhenian Sea by using a reaction\u2013diffusion\u2013taxis model. The study is performed, taking into account the seasonal changes of environmental variables, obtained starting from experimental findings. The multiplicative noise source, present in all three models, mimics the random fluctuations of temperature and velocity field. The vertical profiles of chlorophyll concentration obtained from the stochastic models show a good agreement with experimental data sampled in the two marine sites considered. The results could be useful to devise a new class of models based on a stochastic approach and able to predict future changes in biomass primary production