Generating function for a multiplicative noise with group analysis

Barrera, P.; Ciuchi, S.; Spagnolo, Bernardo

doi:10.1088/0305-4470/26/13/001

Cited by 9 publications

(10 citation statements)

References 11 publications

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“…Thus the multiplicative noise, used in population dynamics and reaction-diffusion problems [78], [86]–[88], within our specific physical and biological context describes the two above mentioned noise sources. These are responsible for the real behaviour of the ecosystem, characterized by an intrinsically non-deterministic dynamics.…”

Section: Methodsmentioning

confidence: 99%

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

et al. 2013

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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.

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Section: Methodsmentioning

confidence: 99%

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

et al. 2013

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“…(16). This value corresponds to the stability-instability transition of the mth moment of the system described by Eq.…”

Section: B Stability Condition In the Case Of Noise With Regulated Pmentioning

confidence: 95%

“…Specifically, random variations of species concentrations in natural ecosystems [1,2,[11][12][13], the role of molecular noise in the growth of bacteria that are present in food products [14], and the stochastic dynamics of diseases connected with genetic mutations [15] are fundamental aspects that cannot be neglected when seeking a better understanding of the dynamics of complex living systems. In particular, in these systems the random variations of temperature, food resources, and other environmental parameters can be described using models in which multiplicative noise sources are present [8,16,17]. In fact, the models that can effectively describe experimental data in population dynamics are those with multiplicative noise, which can give rise to behavior characterized by a power law [9,18,19].…”

Section: Introductionmentioning

confidence: 99%

Stability in a system subject to noise with regulated periodicity

et al. 2011

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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.

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“…Some key questions in population ecology are related to the comprehension of the role that noise, climatic forcing and nonlinear interactions among individuals of the same or different species play on the dynamics of the ecosystems [11,24,25,27,86,93]. Recently researchers devoted more interest and attention to explain the role of noise in different fields of biology [6,10,16,19,21,22,29,32,33,39,41,43,44,68,80,84,89], while investigating noise induced effects on population dynamics [20,49,50,69,70,72].…”

Section: Introductionmentioning

confidence: 99%

“…anchovies and sardines. Our analysis focus on three different ecosystems, in which external random fluctuations are modeled by terms of multiplicative noise [6,21,22]. As a result we find that: (a) in a single compartment ecosystem the presence of a driving force causes stochastic resonance, which results in quasi-periodic oscillations of the two population densities; b) in the same ecosystem it is possible to observe a nonmonotonic behavior of the average extinction time of one species as a function of the noise intensity, i.e.…”

Section: Introductionmentioning

confidence: 99%

Noise Induced Phenomena in the Dynamics of Two Competing Species

Valenti

Giuffrida

Denaro

et al. 2016

Math. Model. Nat. Phenom.

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Abstract. 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 LotkaVolterra 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.

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Generating function for a multiplicative noise with group analysis

Cited by 9 publications

References 11 publications

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

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

Stability in a system subject to noise with regulated periodicity

Noise Induced Phenomena in the Dynamics of Two Competing Species

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