Persistence in nonautonomous predator–prey systems with infinite delays

Teng, Zhidong; Rehim, Mehbuba

doi:10.1016/j.cam.2005.11.006

Cited by 30 publications

(11 citation statements)

References 23 publications

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“…for all t ≥ 0 and κ ≥ P. Let u β (t) be the solution of system (11) with the initial value u β (t) = u(s (n) q , X n ). By (8), (16) and condition of (H 1 ), we have…”

Section: Resultsmentioning

confidence: 98%

Harmless Feedback Control for Permanence and Global Asymptotic Stability in Nonlinear Delay Population Equation

2008

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In this paper, we consider whether or not the feedback control has influence on a nonlinear population equation with several time delays. The general criteria of integrable form on the permanence are established, and we note that the feedback control has no influence to the permanence of system. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global asymptotic stability of any positive solutions to the system.

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“…for all t ≥ 0 and κ ≥ P. Let u β (t) be the solution of system (11) with the initial value u β (t) = u(s (n) q , X n ). By (8), (16) and condition of (H 1 ), we have…”

Section: Resultsmentioning

confidence: 98%

Harmless Feedback Control for Permanence and Global Asymptotic Stability in Nonlinear Delay Population Equation

2008

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“…For results on persistence, permanence and stability for autonomous or non-autonomous Lotka-Volterra with infinite delays, as well as for a biological explanation of the coefficients involved, see [8,10,11,20,21,24,32,33] and references therein. System (5.1) is written in the form (3.1) with F i , G i : BC → R linear operators given by…”

Section: A Cooperative Lotka-volterra Model With Patch Structurementioning

confidence: 99%

“…For alternative techniques for competitive Lotka-Volterra system, see e.g. [1,8,24,32,33]. The second example refers to an FDE modelling the growth of a single or multiple species divided into n classes and following a modified delayed logistic law; the system has unbounded discrete time-varying delays, also includes dispersal terms among the classes, and may be interpreted as a generalization of the modified scalar delayed logistic equation proposed by Arino et al [6].…”

Section: Introductionmentioning

confidence: 98%

Persistence and Permanence for a Class of Functional Differential Equations with Infinite Delay

Faria

2015

J Dyn Diff Equat

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The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with initial conditions that are positive, continuous and bounded. The present method applies to a very broad class of abstract systems of FDEs with infinite delay, both autonomous and non-autonomous, which include many important models used in mathematical biology. Moreover, the hypotheses imposed are in general very easy to check. The results are illustrated with some selected examples.

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“…There is an extensive literature concerning the dynamics of various population interactions. Here we only mention Bereketoglu and Győri [4], He [5], Kuang and Smith [6], Leung and Zhou [7], Meng and Chen [8] and Teng and Rehim [9] among many others. In particular, the books by Gopalsamy [10] and Kuang [11] provide good references in this area.…”

Section: Introductionmentioning

confidence: 97%

Environmental noise impact on regularity and extinction of population systems with infinite delay

Yin

2012

Journal of Mathematical Analysis and Applications

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a b s t r a c tPopulations of biological species are often subject to different types of environmental noises. These noises play crucial roles and have significant impact on the evolution and biodiversity. To understand the effects of different types of noises on the asymptotic properties of the populations, this paper reveals the influence of inherent net birth noise and the interaction noise among stochastically perturbed population systems. By considering systems with infinite delays, (1) this paper discovers that (a) the interaction noise may suppress the potential explosion and guarantee the existence of the global solution, which yields regularity of the stochastic system, and (b) the inherent net birth noise may lead to extinction of the populations; (2) this paper provides sufficient conditions that ensure the stochastic persistence, stochastic boundedness, and asymptotic polynomial growth of the population system; (3) this paper demonstrates that these asymptotic properties are completely determined by stochastic noises and are independent of other parameters.

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Persistence in nonautonomous predator–prey systems with infinite delays

Cited by 30 publications

References 23 publications

Harmless Feedback Control for Permanence and Global Asymptotic Stability in Nonlinear Delay Population Equation

Harmless Feedback Control for Permanence and Global Asymptotic Stability in Nonlinear Delay Population Equation

Persistence and Permanence for a Class of Functional Differential Equations with Infinite Delay

Environmental noise impact on regularity and extinction of population systems with infinite delay

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