On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Dorini, Fabio Antonio; Cecconello, Moiseis dos Santos; Dorini, Leyza Baldo

doi:10.1016/j.cnsns.2015.09.009

Cited by 81 publications

(72 citation statements)

References 20 publications

(37 reference statements)

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“…Considering the effects of uncertain model parameters in the governing ODE of W t as in Dorini et al [3] can also be possible based on (9), which will be addressed in forthcoming papers.…”

Section: Objective Functionmentioning

confidence: 99%

Finding the optimal opening time of harvesting farmed fishery resources

Yoshioka

Yaegashi

2016

Pac. J. Math. Ind.

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As an application of mathematics to engineering problems, this paper formulates a simple optimal stopping problem to decide the opening time of harvesting farmed fishery resources that maximizes an economic objective function. A sufficient condition for unique existence of the internal optimal opening time is provided and its concrete mathematical analysis is carried out. Comparative statics of the optimal opening time clearly reveals its dependence on the parameters of the farming environment. The problem is finally applied to analyzing management of a commercially important fishery resource in Japan.

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“…Considering the effects of uncertain model parameters in the governing ODE of W t as in Dorini et al [3] can also be possible based on (9), which will be addressed in forthcoming papers.…”

Section: Objective Functionmentioning

confidence: 99%

Finding the optimal opening time of harvesting farmed fishery resources

Yoshioka

Yaegashi

2016

Pac. J. Math. Ind.

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“…There are some recent interesting contributions concerning continuous random modelling in population dynamics. 8,9 Discrete random models have not been widely studied in the literature. Recently, authors of this paper have made several contributions related to Markov models 10,11 and linear difference equations.…”

Section: Introductionmentioning

confidence: 99%

(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications

López

Navarro‐Quiles

Romero

et al. 2019

Math Methods in App Sciences

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The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.

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“…In this paper, we shall go beyond, and we revisit the linear RFDE in order to compute the 1-PDF of its solution stochastic process under mild conditions. Although the computation of the 1-PDF of different classes of random differential equations has been dealt in the extant literature (see Dorini et al, 18 Hussein and Selim, 19 Casabán et al, 20,21 and references therein), to the best of our knowledge, this interesting problem is not been addressed yet. In this spirit, let us consider the following random IVP:…”

Section: Introductionmentioning

confidence: 99%

A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique

Burgos

Calatayud

López

et al. 2018

Math Methods in App Sciences

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This paper provides a full probabilistic solution of the randomized fractional linear nonhomogeneous differential equation with a random initial condition via the computation of the first probability density function of the solution stochastic process. To account for most generality in our analysis, we assume that uncertainty appears in all input parameters (diffusion coefficient, source term, and initial condition) and that a wide range of probabilistic distributions can be assigned to these parameters. Throughout our study, we will consider that the fractional order of Caputo derivative lies in ]0,1], that corresponds to the main standard case. To conduct our analysis, we take advantage of the random variable transformation technique to construct approximations of the first probability density function of the solution process from a suitable infinite series representation. We then prove these approximations do converge to the exact density assuming mild conditions on random input parameters. Our theoretical findings are illustrated through 2 numerical examples. KEYWORDSfirst probability density function, random fractional differential equations, random variable transformation technique

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On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Cited by 81 publications

References 20 publications

Finding the optimal opening time of harvesting farmed fishery resources

Finding the optimal opening time of harvesting farmed fishery resources

(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications

A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique

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