Stochastic analysis of prey-predator model with stage structure for prey

Saha, Tapan Kumar; Chakrabarti, C. G.

doi:10.1007/s12190-009-0351-5

Cited by 9 publications

(5 citation statements)

References 12 publications

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“…Indeed, in growth phenomena, various authors have introduced stochastic versions of classical deterministic growth models especially in animal or cell populations, birth-death, energy, survival populations, life-testing experiments, and environmental studies. See, for example: Saha and Chakrabarti [5], Nafidi et al [6], Di Crescenzo and Paraggio [7], Gutiérrez et al [8], and Skiadas and Giovanis [9]. Diffusion processes are also examined in the field of electricity; in fact, many studies have been focused on the consumption of electrical energy; diverse works suggested a means of using stochastic diffusion processes to model the total consumption of electrical power and to forecast the consumption of electrical energy in relation to particular economic or climatologic variables, using statistical techniques.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

2019

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In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan–Schwartz diffusion process to study the evolution of electricity net consumption in Morocco.

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Section: Introductionmentioning

confidence: 99%

Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

2019

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“…And the second one is to add randomly fluctuating driving force directly to the deterministic equations without affecting any particular parameter to incorporate the effect of randomly fluctuating environment ( [13,14]). This type of stochastic perturbation technique to study the effect of fluctuating environment was first introduced by Beretta et al [15] on a population model system, and Shaikhet [16] and then other researchers used it [17].…”

Section: Introductionmentioning

confidence: 99%

Stochastic bifurcation analysis in Brusselator system with white noise

Zhang

2019

Adv Differ Equ

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In this paper, we mainly study the stochastic stability and stochastic bifurcation of Brusselator system with multiplicative white noise. Firstly, by a polar coordinate transformation and a stochastic averaging method, the original system is transformed into an Itô averaging diffusion system. Secondly, we apply the largest Lyapunov exponent and the singular boundary theory to analyze the stochastic local and global stability. Thirdly, by means of the properties of invariant measures, the stochastic dynamical bifurcations of stochastic averaging Itô diffusion equation associated with the original system is considered. And we investigate the phenomenological bifurcation by analyzing the associated Fokker–Planck equation. We will show that, from the view point of random dynamical systems, the noise “destroys” the deterministic stability. Finally, an example is given to illustrate the effectiveness of our analyzing procedure.

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“…These random factors of the environment are not only an integral part of any realistic ecosystem, but they also may lead to complete extinction of populations. The existing research works have investigated dynamic properties of stochastic predator-prey models [7][8][9][10][11][12], stochastic competitive models [13][14][15][16][17][18], stochastic mutualism models [19][20][21][22][23][24] and stochastic three-species models [25][26][27][28][29][30][31][32][33]. To the best of our knowledge, there are few studies to analyze the dynamics of a stochastic cooperation-competition model.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a stochastic cooperation-competition model

et al. 2018

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In this paper, we explore dynamic properties of a stochastic cooperation-competition model. Some sufficient conditions are established for stochastic persistence and stochastic extinction of species. Studies suggest that the noise may have a positive effect on the persistence of species. We also analyze global asymptotic stability of positive solutions and give a stationary distribution of this stochastic model which has the ergodic property. Finally, some numerical simulations are presented to illustrate or complement our mathematical findings.

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Stochastic analysis of prey-predator model with stage structure for prey

Cited by 9 publications

References 12 publications

Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Stochastic bifurcation analysis in Brusselator system with white noise

Analysis of a stochastic cooperation-competition model

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