Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments

Nakata, Yukihiko

doi:10.1016/j.na.2010.06.081

Cited by 7 publications

(1 citation statement)

References 21 publications

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“…There exists an intensive theoretical research in DEPCAG equations (see, for instance, the monographies [1,11,34]), which has been accompanied with applications in engineering, life sciences and numerical analysis of ODE-DDE systems [3,9,13,14,21,26,29,32,33,37]. 1.1.…”

Section: Introductionmentioning

confidence: 99%

A Grobman–Hartman Theorem for Differential Equations with Piecewise Constant Arguments of Mixed Type

Pinto

Robledo

2018

Z. Anal. Anwend.

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We obtain sufficient conditions ensuring the existence of a uniformly continuous and Hölder continuous homeomorphism between the solutions of a linear system of differential equations with piecewise constant argument of generalized type and the solutions of the quasilinear corresponding system. We use a definition (recently introduced by M. Akhmet) of exponential dichotomy for those systems combined with technical assumptions on the nonlinear part. Our result generalizes a previous work of G. Papaschinopoulos.

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Section: Introductionmentioning

confidence: 99%

A Grobman–Hartman Theorem for Differential Equations with Piecewise Constant Arguments of Mixed Type

Pinto

Robledo

2018

Z. Anal. Anwend.

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Boundness and Linearisation of a Class of Differential Equations with Piecewise Constant Argument

Zou

Xia

Pinto

et al. 2018

Qual. Theory Dyn. Syst.

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The differential equations with piecewise constant argument (DE-PCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded, we study the bounded solution and global topological linearisation of a class of DEPCAs of general type. One of the purpose of this paper is to obtain a new criterion for the existence of a unique bounded solution, which improved the previous results. The other aim of this paper is to establish a generalized Grobman-Hartman result for the topological conjugacy between a nonlinear perturbation system and its linear system. The method is based on the new obtained criterion for bounded solution. The obtained results generalized and improved some previous papers. Some novel techniques are employed.

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3/2 -stability conditions for a class of Volterra–Levin equations

Zhao

Yuan

2014

Nonlinear Analysis: Theory, Methods & Applications

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Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments

Cited by 7 publications

References 21 publications

A Grobman–Hartman Theorem for Differential Equations with Piecewise Constant Arguments of Mixed Type

A Grobman–Hartman Theorem for Differential Equations with Piecewise Constant Arguments of Mixed Type

Boundness and Linearisation of a Class of Differential Equations with Piecewise Constant Argument

3/2 -stability conditions for a class of Volterra–Levin equations

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