11 results on '"*DELAY differential equations"'
Search Results
2. On the qualitative behaviors of stochastic delay integro-differential equations of second order.
- Author
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Mahmoud, Ayman M. and Tunç, Cemil
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INTEGRO-differential equations , *DELAY differential equations - Abstract
In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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3. Hopf bifurcation and normal form in a delayed oncolytic model.
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Najm, Fatiha, Ahmed, Moussaid, Yafia, Radouane, Aziz Alaoui, M. A., and Boukrim, Lahcen
- Abstract
In this paper, we investigate the mathematical analysis of a mathematical model describing the virotherapy treatment of a cancer with logistic growth and the effect of viral cycle presented by a time delay. The cancer population size is divided into uninfected and infected compartments. Depending on time delay, we prove the positivity and boundedness and the stability of equilibria. We give conditions on which the viral cycle leads to “Jeff’s phenomenon” observed in laboratory and causes oscillations in cancer size via Hopf bifurcation theory. We establish an algorithm that determines the bifurcation elements via center manifold and normal form theories. We give conditions which lead to a supercritical or subcritical bifurcation. We end with numerical simulations illustrating our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. Stability of impulsive stochastic functional differential equations with delays.
- Author
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Guo, Jingxian, Xiao, Shuihong, and Li, Jianli
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DELAY differential equations , *STOCHASTIC differential equations , *FUNCTIONAL differential equations , *IMPULSIVE differential equations , *STABILITY criterion , *LYAPUNOV functions - Abstract
In this paper, we consider the global asymptotical stability of stochastic functional differential equations with impulsive effects. First, by constructing the Lyapunov function, some stability criteria of impulsive stochastic functional differential equations are established. Second, we propose an application to investigate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]
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- 2024
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5. Numerical investigation of two fractional operators for time fractional delay differential equation.
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Chawla, Reetika, Kumar, Devendra, and Baleanu, Dumitru
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FRACTIONAL differential equations , *DELAY differential equations , *NUMERICAL analysis - Abstract
This article compared two high-order numerical schemes for convection-diffusion delay differential equation via two fractional operators with singular kernels. The objective is to present two effective schemes that give (3-α)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(3-\alpha )$$\end{document} and second order of accuracy in the time direction when α∈(0,1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha \in (0,1)$$\end{document} using Caputo and Modified Atangana-Baleanu Caputo derivatives, respectively. We also implemented a trigonometric spline technique in the space direction, giving second order of accuracy. Moreover, meticulous analysis shows these numerical schemes to be unconditionally stable and convergent. The efficiency and reliability of these schemes are illustrated by numerical experiments. The tabulated results obtained from test examples have also shown the comparison of these operators. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Lévy jumps under different structures.
- Author
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Song, Ruili, Zhao, Jiayu, and Zhu, Quanxin
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STOCHASTIC differential equations , *HYBRID systems , *EXPONENTIAL stability , *DELAY differential equations , *LYAPUNOV functions , *MATRICES (Mathematics) - Abstract
This paper investigates the boundedness and stability of a class of nonlinear hybrid neutral stochastic differential delay systems with Lévy jumps and different structures. The coefficients in this system satisfy the local Lipschitz condition and a suitable Khasminskii-type condition, and the state space of the system is separated into two subsets, the existence uniqueness, asymptotic boundedness, and exponential stability of the system are obtained by designing a new Lyapunov function and applying the M-matrix technique as well as dealing with the non-differentiable delay function. Different with the existing work, we not only consider the neutral term, but also the case of the delay function being bounded and non-differentiable. At last, numerical examples are performed to manifest the obtained results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability.
- Author
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Saedshoar Heris, Mahdi and Javidi, Mohammad
- Abstract
In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of O(h2+k2+κ2+σ2+ρ2)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textrm{O}({h^2} + {k^2} +{\kappa ^2} + {\sigma ^2} + {\rho ^2})$$\end{document}, where
h ,k and κ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\kappa$$\end{document} are space step forx ,y and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution. [ABSTRACT FROM AUTHOR]- Published
- 2024
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8. Delay differential equation modeling of social contagion with higher-order interactions.
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Lv, Xijian, Fan, Dongmei, Yang, Junxian, Li, Qiang, and Zhou, Li
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CONTAGION (Social psychology) , *SOCIAL interaction , *SOCIAL values , *SYSTEM dynamics , *DELAY differential equations - Abstract
In this paper, we propose a social contagion model with group interactions on heterogeneous network, in which the group interactions are represented by incorporating higher-order terms. The dynamics of the proposed model are analyzed, revealing the effect of group interactions on the system dynamics. We derive a global asymptotically stability condition of the zero equilibrium point. If the parameters enhancement factor and transform probability meet the condition, the social contagion will eventually disappear. The bifurcation behavior arising from group interactions is investigated, when the enhancement factor exceeds a threshold, the system undergoes a backward bifurcation. This implies that R 0 < 1 does not guarantee the disappearance of social contagion, we also need to control the initial values of social contagion at a lower level. The optimal control strategies for the model are provided. Moreover, the numerical simulations validate the accuracy of the theoretical analysis. It is worth noting that the group interactions lead to the emergence of a bistable phenomenon, in which the social contagion will either fade away or persist eventually, depending on the initial values. • The simplicial SIS social contagion model with delay is proposed on heterogeneous networks. • The dynamics of the model are analyzed, revealing the effect of group interactions on the system dynamics. • An optimal control strategy is proposed for the model, incorporating group interactions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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9. Stability prediction via parameter estimation from milling time series.
- Author
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Turner, James D., Moore, Samuel A., and Mann, Brian P.
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DELAY differential equations , *SPECTRAL element method , *VIBRATION (Mechanics) , *MACHINE tools , *FORECASTING , *PARAMETER estimation - Abstract
Machine tool vibrations impose severe limitations on industry. Recent progress in solving for the stability behavior of delay differential equations and in modeling milling operations with time delay differential equations has provided the potential to significantly reduce the aforementioned limitations. However, industry has yet to widely adopt the current academic knowledge due to the cost barriers in implementing this knowledge. Some of these cost prohibitive tasks include time-consuming experimental cutting tests used to calibrate model force parameters and experimental modal tests for every combination of tool, tool holder, tool length, spindle, and machine. This paper introduces an alternative approach whereby the vibration behavior of a milling tool during cutting is used to obtain the necessary model parameters for the common delay differential equation models of milling. • Method to estimate milling model parameters from experimental time series. • Estimated parameters used to predict stability chart for range of cutting conditions. • Stability predictions show close match with experimental results. • Extends the spectral element method to incorporate steady-state vibration. • Automated approach for instrumented milling that makes manual modal test unnecessary. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. Stability of coupled Wilson–Cowan systems with distributed delays.
- Author
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Kaslik, Eva, Kökövics, Emanuel-Attila, and Rădulescu, Anca
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GAMMA distributions , *LARGE-scale brain networks , *BASAL ganglia , *DYNAMICAL systems , *DELAY differential equations - Abstract
Building upon our previous work on the Wilson-Cowan equations with distributed delays (Kaslik et al., 2022), we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the transitions in and out of oscillatory regimes associated with pathological behavior. We investigate these mechanisms under multiple coupling scenarios, and we compare the effects of using discrete delays versus a weak Gamma delay distribution. We found that, in order to trigger and stop oscillations, each kernel emphasizes different critical combinations of coupling weights and time delay, with the weak Gamma kernel restricting oscillations to a tighter locus of coupling strengths, and to a limited range of time delays. We finally illustrate the general analytical results with simulations for two particular applications: generation of beta-rhythms in the basal ganglia, and alpha oscillations in the prefrontal-limbic system. • We study long-term dynamics in coupled Wilson–Cowan systems with distributed delays. • Our analysis focuses on understanding the system's transitions in and out of stable oscillations. • We study how these transitions change under different connectivity schemes and strengths. • We explore the effects of different delay distributions and average delay values. • The analysis is illustrated with simulations in two different functional brain networks. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
11. Numerical stability analysis of spatial-temporal fully discrete scheme for time-fractional delay Schrödinger equations.
- Author
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Yao, Zichen and Yang, Zhanwen
- Abstract
We consider the numerical stability problem for fractional delay Schrödinger equations involving a Caputo fractional derivative in time, which is developed by Galerkin finite element method (FEM) in space and fractional linear multistep methods (FLMMs) in time. Through rigorous analyses of the characteristic equation yielded by the Laplace transform, we first present an α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{\alpha }$$\end{document}-dependent coefficient criterion to ensure the stability of spatially semidiscrete Galerkin FEM and extend the stability property to all convergent spatially semidiscrete methods. Secondly, by introducing a decoupling technique after Z\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{\mathcal {Z}}$$\end{document} transform, we prove the stability of FLMMs generated by both A-stable and A(β\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{\beta }$$\end{document})-stable linear multistep methods, without any restriction on the time step size. The stability results are formulated by the fractional exponent, the principal eigenvalue of Dirichlet Laplacian, and the mesh size, but are not related to the delay and time step size. However, for a general spatial region, the principal eigenvalue of Dirichlet Laplacian is always unavailable. In order to provide an effective method for stability detection, when the stability condition is violated, we prove that the fractional trapezoidal rule is an effective method to detect stability because it can not only maintain the stable behavior of the semidiscrete solution, but also the unstable behavior. Extensive numerical experiments for fractional delay Schrödinger equations confirm the long-time decay behaviors of the fully discrete numerical solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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