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1
Content available remote

Permanence for a delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term

100%
Liu B.
Annales Polonici Mathematici
|
2011
|
tom 101
|
nr 2
123-129
EN
We study a generalized Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we employ a novel proof to establish some criteria guaranteeing the permanence of this model. Moreover, we give an example to illustrate our main result.
2
Content available remote

Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

100%
Liu B.
Annales Polonici Mathematici
|
2016
|
tom 116
|
nr 2
155-171
EN
This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.
3
Content available remote

New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model

100%
Liu B.
Annales Polonici Mathematici
|
2015
|
tom 113
|
nr 2
191-208
EN
This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays, which is defined on the nonnegative function space. Under appropriate conditions, we establish some criteria to ensure that all solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give an example with numerical simulations to illustrate our main results.
4
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Existence and uniqueness of periodic solutions for a kind of Duffing equation with two deviating arguments

100%
Liu B.
Annales Polonici Mathematici
|
2006
|
tom 89
|
nr 3
247-258
EN
We use the coincidence degree to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Duffing equation with two deviating arguments of the form x'' + Cx'(t) + g₁(t,x(t-τ₁(t))) + g₂(t,x(t-τ₂(t))) = p(t).
5
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Existence and uniqueness of positive periodic solutions of delayed Nicholson's blowflies models

64%
Long F., Liu B.
Annales Polonici Mathematici
|
2012
|
tom 103
|
nr 3
217-228
EN
This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays. By applying the coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, a totally new approach to proving the uniqueness of positive periodic solutions is proposed. In particular, an example is employed to illustrate the main results.
6
Content available remote

Periodic solutions for some delay differential equations appearing in models of power systems

64%
Liu B., Huang L.
Annales Polonici Mathematici
|
2005
|
tom 86
|
nr 2
153-164
EN
The authors use coincidence degree theory to establish some new results on the existence of T-periodic solutions for the delay differential equation x''(t) + a₁x'(t) + a₂(xⁿ(t))' + a₃x(t)+ a₄x(t-τ) + a₅xⁿ(t) + a₆xⁿ(t-τ) = f(t), which appears in a model of a power system. These results are of practical significance.
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