Stability in mean for uncertain delay differential equations based on new Lipschitz conditions

Uncertain delay differential equations (UDDEs) charactered by Liu process can be employed to model an uncertain control system with a delay time. The stability of its solution always be a significant matter. At present, the stability in measure for UDDEs has been proposed and investigated based on the strong Lipschitz condition. In reality, the strong Lipschitz condition is so strictly and hardly applied to judge the stability in measure for UDDEs. For the sake of solving the above issue, the stability in measure based on new Lipschitz condition as a larger scale of applications is verified in this paper. In other words, if it satisfies the strong Lipschitz condition, it must satisfy the new Lipschitz conditions. Conversely, it may not be established. An example is provided to show that it is stable in measure based on the new Lipschitz conditions, but it becomes invalid based on the strong Lipschitz condition. Moreover, a special class of UDDEs is verified to be stable in measure without any limited condition. Besides, some examples are investigated in this paper.

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On strong convergence of explicit numerical methods for stochastic delay differential equations under non-global Lipschitz conditions

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113079 ◽

2021 ◽

Vol 382 ◽

pp. 113079 ◽

Cited By ~ 1

Author(s):

Wanrong Cao ◽

Jia Liang ◽

Yufen Liu

Keyword(s):

Numerical Methods ◽

Differential Equations ◽

Strong Convergence ◽

Delay Differential Equations ◽

Stochastic Delay Differential Equations ◽

Stochastic Delay ◽

Delay Differential ◽

Lipschitz Conditions

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Delay Differential Equations - With Applications in Population Dynamics

10.1016/s0076-5392(08)x6164-8 ◽

1993 ◽

Keyword(s):

Population Dynamics ◽

Differential Equations ◽

Delay Differential Equations ◽

Delay Differential

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Neutral uncertain delay differential equations

Green Communications and Networks ◽

10.2495/gcn131342 ◽

2014 ◽

Author(s):

Xintong Ge

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Delay Differential

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Growth on Meromorphic Solutions of Non-linear Delay Differential Equations

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/bbms/1553047233 ◽

2019 ◽

Vol 26 (1) ◽

pp. 131-147 ◽

Cited By ~ 2

Author(s):

Pei-Chu Hu ◽

Qiong-Yan Wang

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Meromorphic Solutions ◽

Linear Delay ◽

Non Linear ◽

Delay Differential

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A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽

10.2298/fil1711157a ◽

2017 ◽

Vol 31 (11) ◽

pp. 3157-3172

Author(s):

Mujahid Abbas ◽

Bahru Leyew ◽

Safeer Khan

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Periodic Solutions ◽

Metric Space ◽

Delay Differential Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Existence Of Periodic Solutions ◽

Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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Exponential Decay Estimates For Some Components of Solutions to the Nonlinear Delay Differential Equations of the Living System Models

Siberian Mathematical Journal ◽

10.1134/s0037446620040126 ◽

2020 ◽

Vol 61 (4) ◽

pp. 715-724

Author(s):

N. V. Pertsev

Keyword(s):

Differential Equations ◽

Exponential Decay ◽

Delay Differential Equations ◽

Living System ◽

Decay Estimates ◽

System Models ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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Mass Transport Modelling in Porous Media Using Delay Differential Equations

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.258-260.586 ◽

2006 ◽

Vol 258-260 ◽

pp. 586-591

Author(s):

António Martins ◽

Paulo Laranjeira ◽

Madalena Dias ◽

José Lopes

Keyword(s):

Porous Media ◽

Differential Equations ◽

Mass Transport ◽

Delay Differential Equations ◽

Dispersion Model ◽

Flow Characteristics ◽

Convective Transport ◽

Transport Modelling ◽

Flow Field Characteristics ◽

Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

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