Periodic and almost periodic solution for a non-autonomous epidemic predator-prey system with time-delay

Tian, Baodan; Qiu, Yanhong; Chen, Ning

doi:10.1016/j.amc.2009.06.006

Cited by 7 publications

(6 citation statements)

References 27 publications

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“…Therefore, almost periodicity is a more common phenomenon than strict periodicity. Basing on the above background and the previous model proposed in [21], the authors proposed an ecological epidemic system with impulsive effects and multiple time delays on the model. It is supposed that all of the coefficients of the system are almost periodic, as well.…”

Section: Discussionmentioning

confidence: 99%

“…So it is more reasonable to assume the periodicity or almost periodicity of parameters in the systems. And considering this factor, Tian et al [21] (2)…”

Section: Introductionmentioning

confidence: 99%

“…However, to the best our knowledge, references on the periodic ecoepidemic model with impulsive perturbations seem relatively fewer. Since the rapid development in the theory of the impulsive equations and the functional differential equations (see [21][22][23][24][25][26]), many excellent results have been derived in ecological models, epidemic models, and even neural network models (see [27][28][29][30][31][32][33][34][35][36][37] and so on).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

Tian¹,

Chen

Qiu³

2015

Discrete Dynamics in Nature and Society

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A nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there is an epidemic disease in the predator. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals it is proved that there exists a unique uniformly asymptotically stable almost periodic solution of the system.

show abstract

Section: Discussionmentioning

confidence: 99%

“…So it is more reasonable to assume the periodicity or almost periodicity of parameters in the systems. And considering this factor, Tian et al [21] (2)…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

Tian¹,

Chen

Qiu³

2015

Discrete Dynamics in Nature and Society

Self Cite

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“…Then system (13) has a unique almost periodic solution which is uniformly asymptotically stable. Lemma 2.4 (see [16,17]) For a > 0, b > 0, u(0) = u 0 > 0:…”

Section: Preliminariesmentioning

confidence: 99%

A non-autonomous impulsive food-chain model with delays

Tian

Zhang

et al. 2019

Adv Differ Equ

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A non-autonomous almost periodic prey-predator system with impulsive effects and multiple delays is proposed in this paper, Holling's type-IV systems and ratio-dependent functional responses are also involved in the model. By applying absolute inequalities, integral inequalities, differential inequalities and the mean-value theorem and other mathematical analysis techniques, we obtain some sufficient conditions which guarantee the permanence of the system. Moreover, we obtain the existence and the uniqueness of the almost periodic solution which is uniformly asymptotically stable by constructing a series of Lyapunov functionals. Finally, we present several numerical examples to verify the theoretical results and present some discussions of pest management in the agricultural ecological system.

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“…In [12], a nonautonomous predator-prey system with discrete time delay is studied, where there is epidemic disease in the predator. By using some techniques of the differential inequalities and delay differential inequalities, the permanence of system is discussed under some appropriate conditions.…”

Section: Introductionmentioning

confidence: 99%

Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

Liu

2014

Abstract and Applied Analysis

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We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

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Periodic and almost periodic solution for a non-autonomous epidemic predator-prey system with time-delay

Cited by 7 publications

References 27 publications

Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

A non-autonomous impulsive food-chain model with delays

Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

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