Existence and global attractivity of a periodic solution to a nonautonomous dispersal system with delays

Kouche, Mahiéddine; Tatar, Nasser–eddine

doi:10.1016/j.apm.2005.12.010

Cited by 10 publications

(3 citation statements)

References 20 publications

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“…Since the pioneering theoretical work by Skellam [19], many works have focused on the effect of spatial factors which play a crucial rule in the stability and persistence of a population ( [3,4,[6][7][8][9]12,13] and reference cited therein). Xu et al [4] investigated the following two-species non-autonomous path-system with time delays:…”

Section: Introductionmentioning

confidence: 99%

Positive periodic solutions for impulsive predator–prey model with dispersion and time delays

Liang

Shen

2010

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Positive periodic solutions for impulsive predator–prey model with dispersion and time delays

Liang

Shen

2010

Applied Mathematics and Computation

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“…To obtain the sufficient conditions for the existence of positive periodic solution, we first summarize some important results from [49][50][51][52][53] that will be basic for this section.…”

Section: Existence Of Periodic Solutionmentioning

confidence: 99%

Existence and global stability of positive periodic solution of tri-trophic food chain with middle predator migratory in nature

Samanta

Alquran

Chattopadhyay

2015

Applied Mathematical Modelling

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a b s t r a c tPredator avoidance is the most important factor inducing vertical migration among zooplankton. Light intensity at the surface water also plays an important role to shape the predation pressure on zooplankton as most of the fishes show visually oriented predation. In the present paper, we assume that zooplankton can switch between vulnerable and invulnerable state through vertical migration. This switching is regulated by light intensity, predator abundance and food abundance in surface water. We propose a tri-trophic food chain model incorporating migratory behavior of middle predator. Further, we study the non-autonomous version of the proposed model by incorporating the seasonal variation of the rate parameters of the model. The sufficient conditions for the existence of positive periodic solutions are obtained. We also obtain the conditions for the global attractivity of positive periodic solutions. The numerical experiments are carried out to substantiate analytical findings.

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“…Hui and Zhu (2005); Arenas et al (2008a); Xia et al (2007). In addition some authors have been studied periodic solutions for other population mathematical models, see Huoa et al (2007); Kouche and Tatar (2007).…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of childhood obesity from a social epidemic point of view for the spanish region of Valencia: numerical and analytical solutions.

Parra¹,

Carlos²

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Existence and global attractivity of a periodic solution to a nonautonomous dispersal system with delays

Cited by 10 publications

References 20 publications

Positive periodic solutions for impulsive predator–prey model with dispersion and time delays

Positive periodic solutions for impulsive predator–prey model with dispersion and time delays

Existence and global stability of positive periodic solution of tri-trophic food chain with middle predator migratory in nature

Mathematical modeling of childhood obesity from a social epidemic point of view for the spanish region of Valencia: numerical and analytical solutions.

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