On stability of cooperative and hereditary systems with a distributed delay

Berezansky, Leonid; Braverman, Elena

doi:10.1088/0951-7715/28/6/1745

Cited by 4 publications

(10 citation statements)

References 29 publications

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“…Next, we check that conditions (A 0 )-(A 6 ) of Theorem 2.4 are satisfied for the System (51). First note that we can rewrite (51) in the form (5) with…”

Section: Boundedness Of Positive Solutions Of a System Of Nonlinear Dmentioning

confidence: 99%

“…. This manuscript extends the method introduced for the scalar case in [21] to the nonlinear delay system (5). A key element of the proof of our Theorem 2.4 is a result proved in [22], where sufficient conditions are formulated implying that a certain nonlinear algebraic system associated to (5) has a unique positive solution (see Lemma 2.3 and Theorem 4.2 below).…”

mentioning

confidence: 93%

“…The structure of our paper is the following. In Section 2 we formulate our main results: Theorem 2.4 below gives estimates for the limit inferior and limit superior of the positive solutions of System (5). In Section 3 we show several corollaries of our main results and numerical examples.…”

mentioning

confidence: 98%

“…Global stability of a positive equilibrium and oscillations of the solutions were investigated depending on the values of a parameter in the formula of the positive nonlinear function f . In [5] the two-dimensional systeṁ…”

mentioning

confidence: 99%

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Boundedness of positive solutions of a system of nonlinear delay differential equations

Győri¹,

Hartung²,

Mohamady

2018

Discrete &Amp; Continuous Dynamical Systems - B

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In this manuscript the system of nonlinear delay differential equationsẋ i (t) = n j=1 n 0 =1 α ij (t)h ij (x j (t − τ ij (t))) − β i (t)f i (x i (t)) + ρ i (t), t ≥ 0, 1 ≤ i ≤ n is considered. Sufficient conditions are established for the uniform permanence of the positive solutions of the system. In several particular cases, explicit formulas are given for the estimates of the upper and lower limit of the solutions. In a special case, the asymptotic equivalence of the solutions is investigated.

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“…Next, we check that conditions (A 0 )-(A 6 ) of Theorem 2.4 are satisfied for the System (51). First note that we can rewrite (51) in the form (5) with…”

Section: Boundedness Of Positive Solutions Of a System Of Nonlinear Dmentioning

confidence: 99%

mentioning

confidence: 93%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Boundedness of positive solutions of a system of nonlinear delay differential equations

Győri¹,

Hartung²,

Mohamady

2018

Discrete &Amp; Continuous Dynamical Systems - B

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“…For several real applications of this model, such as neuron networks and Lotka-Volterra cooperative systems, see [28] and references therein. Theorem 8.…”

Section: A Planar System With Distributed Delaysmentioning

confidence: 99%

Permanence for Nonautonomous Differential Systems with Delays in the Linear and Nonlinear Terms

Faria

2021

Mathematics

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In this paper, we obtain sufficient conditions for the persistence and permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed delays in both the linear and nonlinear terms, and where typically the nonlinear terms are nonmonotone. Applications to systems inspired by mathematical biology models are given.

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On the global attractivity of non-autonomous neural networks with a distributed delay

Berezansky

Braverman

2021

Nonlinearity

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We consider a system of s nonlinear differential equations with a distributed] and obtain global asymptotic stability conditions, which are independent of delays. The ideas of the proofs are based on the notion of a strong attractor of a vector difference equation associated with a nonlinear vector differential equation. The results are applied to Hopfield neural networks and to compartment-type models of population dynamics with Nicholson's blowflies growth law.

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On stability of cooperative and hereditary systems with a distributed delay

Cited by 4 publications

References 29 publications

Boundedness of positive solutions of a system of nonlinear delay differential equations

Boundedness of positive solutions of a system of nonlinear delay differential equations

Permanence for Nonautonomous Differential Systems with Delays in the Linear and Nonlinear Terms

On the global attractivity of non-autonomous neural networks with a distributed delay

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