Positive almost periodic solution for impulsive Nicholson's blowflies model with multiple linear harvesting terms

A Nicholson's blowflies model with feedback control and time delay is studied. By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. It is proved that the feedback control variable and time delay have no influence on the permanence and extinction of the system.

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Existence and exponential stability of the unique positive almost periodic solution for impulsive Nicholson’s blowflies model with linear harvesting term

Applied Mathematical Modelling ◽

10.1016/j.apm.2015.03.002 ◽

2015 ◽

Vol 39 (23-24) ◽

pp. 7124-7133 ◽

Cited By ~ 5

Author(s):

Zhijian Yao

Keyword(s):

Periodic Solution ◽

Exponential Stability ◽

Almost Periodic Solution ◽

Almost Periodic ◽

Nicholson’S Blowflies Model ◽

Positive Almost Periodic Solution ◽

Linear Harvesting Term

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Positive almost periodic solution for a class of Nicholson’s blowflies model with a linear harvesting term

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2011.08.009 ◽

2012 ◽

Vol 13 (2) ◽

pp. 686-693 ◽

Cited By ~ 25

Author(s):

Fei Long

Keyword(s):

Periodic Solution ◽

Almost Periodic Solution ◽

Almost Periodic ◽

Nicholson’S Blowflies Model ◽

Positive Almost Periodic Solution ◽

Linear Harvesting Term

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Existence of a positive almost periodic solution for a nonlinear delay integral equation

Nonlinear Analysis ◽

10.1016/j.na.2011.05.045 ◽

2011 ◽

Vol 74 (16) ◽

pp. 5600-5605 ◽

Cited By ~ 6

Author(s):

Bin Xu ◽

Qingye Zhang

Keyword(s):

Integral Equation ◽

Periodic Solution ◽

Almost Periodic Solution ◽

Almost Periodic ◽

Delay Integral Equation ◽

Positive Almost Periodic Solution ◽

Nonlinear Delay

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New results on existence and exponential stability of the unique positive almost periodic solution for Hematopoiesis model

Applied Mathematical Modelling ◽

10.1016/j.apm.2015.03.003 ◽

2015 ◽

Vol 39 (23-24) ◽

pp. 7113-7123 ◽

Cited By ~ 7

Author(s):

Zhijian Yao

Keyword(s):

Periodic Solution ◽

Exponential Stability ◽

Almost Periodic Solution ◽

Almost Periodic ◽

Positive Almost Periodic Solution ◽

Hematopoiesis Model

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Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2010.12.010 ◽

2011 ◽

Vol 12 (4) ◽

pp. 1938-1949 ◽

Cited By ~ 32

Author(s):

Wentao Wang ◽

Lijuan Wang ◽

Wei Chen

Keyword(s):

Periodic Solution ◽

Exponential Stability ◽

Almost Periodic Solution ◽

Delay Systems ◽

Almost Periodic ◽

Positive Almost Periodic Solution

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Dynamics of a non-autonomous ratio-dependent predator—prey system

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500002304 ◽

2003 ◽

Vol 133 (1) ◽

pp. 97-118 ◽

Cited By ~ 60

Author(s):

Meng Fan ◽

Qian Wang ◽

Xingfu Zou

Keyword(s):

Periodic Solution ◽

Asymptotic Stability ◽

Positive Periodic Solution ◽

Almost Periodic Solution ◽

Almost Periodic ◽

Predator Prey ◽

Prey System ◽

Autonomous Case ◽

Positive Almost Periodic Solution ◽

Ratio Dependent

We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

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