On asymptotic stability for linear delay equations

Huang, Wen Zhang

doi:10.57262/die/1371154289

Cited by 6 publications

(3 citation statements)

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“…In recent years, model (1.1) has been investigated extensively by many researchers and many interesting results have also been obtained (see e.g. [3,8,9,14]). For example, Green and Stech [8] investigated the existence and local stability of a positive steady state solution bifurcating from the zero solution, and the corresponding stability results were improved by Huang [9].…”

Section: Introductionmentioning

confidence: 99%

“…[3,8,9,14]). For example, Green and Stech [8] investigated the existence and local stability of a positive steady state solution bifurcating from the zero solution, and the corresponding stability results were improved by Huang [9]. As pointed out by Huang [10], zero-Dirichlet boundary conditions imposed on (1.1) lead to the fact that the nontrivial steady state solutions and periodic solutions (if they exist) of (1.1) are spatially heterogeneous.…”

Section: Introductionmentioning

confidence: 99%

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Stability of bifurcating periodic solutions in a delayed reaction–diffusion population model

Yan

2010

Nonlinearity

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A delayed reaction-diffusion model of the Fisher type with a single discrete delay and zero-Dirichlet boundary conditions on a general bounded open spatial domain with a smooth boundary is considered. The stability of a spatially heterogeneous positive steady state solution and the existence of Hopf bifurcation about this positive steady state solution are investigated. In particular, by using the normal form theory and the centre manifold reduction for partial functional differential equations, the stability of bifurcating periodic solutions occurring through Hopf bifurcations is investigated. It is demonstrated that the bifurcating periodic solution occurring at the first bifurcation point is orbitally asymptotically stable while those occurring at the other bifurcation points are unstable.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of bifurcating periodic solutions in a delayed reaction–diffusion population model

Yan

2010

Nonlinearity

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“…For the one-dimensional case, the compressible micropolar ideal gas model was first described by Mujaković (see [31]), and then the local existence, global existence, regularity, large time behavior, stity of the solution, and the existence of global attractors for the nonisentropic compressible micropolar ideal gas model were established in [6,13,25,28,32,33,34,35,36,37,42]. Recently, there have been several investigations on the global existence, uniqueness, regularity, and large time behavior of solutions to problems associated with the compressible micropolar real gas model in [8,2,3,4,23]. In addition, for the isentropic micropolar fluid model, we would like to refer to the studies in [5].…”

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confidence: 99%

Large-time behavior of solutions to the compressible micropolar fluid with shear viscosity

Huang,

Bian,

Chen

2024

DCDS-S

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Stability and Bifurcation in Delay–Differential Equations with Two Delays

Li¹,

Ruan

Wei

1999

Journal of Mathematical Analysis and Applications

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The purpose of this paper is to study a class of differential᎐difference equations with two delays. First, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. General stability criteria involving the delays and the parameters are obtained. Second, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits the Hopf bifurcation. The stability of the bifurcating periodic solutions are determined by using the center manifold theorem and the normal form theory. Finally, as an example, we analyze a simple motor control equation with two delays. Our results improve some of the existing results on this equation. ᮊ

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On asymptotic stability for linear delay equations

Cited by 6 publications

References 1 publication

Stability of bifurcating periodic solutions in a delayed reaction–diffusion population model

Stability of bifurcating periodic solutions in a delayed reaction–diffusion population model

Large-time behavior of solutions to the compressible micropolar fluid with shear viscosity

Stability and Bifurcation in Delay–Differential Equations with Two Delays

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